FRIEDMAN, Senior Circuit Judge.

The Court of Federal Claims held that the proceedings by which an Army Board recommended the involuntary retirement of certain Army officers were constitutionally invalid because of instructions by the Secretary of the Army that the Board give minority and female officers preferential treatment. The court further held that the harmless error concept was inapplicable in this case. The result of the latter ruling was that many non-retained white male officers who would not have been retained even if the Board had not given preferential treatment to minority and female officers, nevertheless would be reinstated as of the date of their involuntary retirement and receive back pay to that date. The government here challenges only the court's harmless error ruling. We reverse that ruling.

I

A. The facts forming the background of this suit, as found by the Court of Federal Claims, Christian v. United States, 46 Fed. Cl. 793, 798-99 (2000), and as supplemented by the record, are undisputed.

In 1992, the Secretary of the Army ("Secretary") convened a Selective Early Retirement Board ("Retirement Board"), pursuant to 10 U.S.C. §§ 611, 638, to recommend Army lieutenant colonels for involuntary early retirement. The Secretary issued lengthy detailed instructions to the Board, which was told to select for early retirement a "minimum" of 1210 officers and an "optimum" of 1452. (The Board reported that it recommended 1169 officers for early retirement.) "[B]ased on the guidance" in the instructions, the Retirement Board was directed to "determine which officers to recommend for selective early retirement by first determining an order of merit list of the officers considered."

One section of the instructions, captioned " Minority and Female Officers," included the following provisions:

a. The Army is firmly committed to providing equal opportunity for minority and female officers in all facets of their career development, utilization, and progression. The goal for this board is to achieve a percent of minority and female officers recommended for early retirement not greater than the rate for all officers in the zone of consideration. This goal is important because, to the extent that each board achieves it, the Army at large will have a clear perception of equal opportunity and the officers not recommended for early retirement will enjoy the opportunity for continued career progression to the benefit of the Army. This goal is not intended as guidance for you to meet any "quota."

b. In evaluating the records of minority and female officers, the board should consider that past personal and institutional discrimination may have disadvantaged minority and female officers. Such discrimination may include, but certainly is not limited to, disproportionately lower evaluation reports, assignments of lesser importance or responsibility, and lack of opportunity to attend career-building military schools. Take these factors into consideration in evaluating these officers' potential to make continued significant contributions to the Army.

c. Prior to recess, the board (in the report of officers recommended for early retirement) must review and report the extent to which minority and female officers were recommended at a rate greater than males and non-minority officers.

The instructions specified four "phases of deliberation" through which the Retirement Board should proceed. For phase two, in which it was to "Evaluate minority and female goal attainment," the following directive was included:

(2) If there are adverse deviations in the minority or female selection rates overall or within a specific career field, the board will reevaluate and may revote the files of the minority and female officers keeping in mind the factors contained in paragraph 4 of Enclosure 1. After revoting an officer's record, the relative standing will be adjusted.

The Retirement Board's proceedings for early retirement involved 4522 lieutenant colonels. In making its recommendations, the Retirement Board followed the four-phase procedure, only the first two steps of which are relevant here.

In phase one, the Retirement Board reviewed and evaluated the officers' records and based thereon established the comprehensive "order of merit," as directed by the Secretary's instructions. In phase two, the Retirement Board determined the "optimum number" of officers to be recommended for early retirement and then applied that number to determine the dividing line on the "order of merit" list between those to be retained and those to be retired.

At the conclusion of the phase two determinations, the percentage of minority officers to be retired was greater than the overall retirement rate for all officers. The Retirement Board then reevaluated the records of the minority officers, and selected a number of them for retention. It recommended 1052 white male lieutenant colonels for early retirement, with 3067 retained; and 131 minority and female officers for early retirement, with 341 retained. (There may be some overlap within these categories.)

In its "After-Action Report," the Retirement Board stated that in its initial determinations in phase one:

The Board did not meet its minority selection goal. Minority officers were selected for early retirement at a rate of 29 percent in comparison to the overall selection rate of 25.8 percent. Upon completion of the Board's initial deliberations, it reevaluated minority officer files. The Board identified some minority officers whose records warranted reconsideration to ensure they had not been disadvantaged by past personal or institutional bias. A revote was conducted resulting in a number of minority officers being selected for retention on active duty.

B. The appellee Christian, a white lieutenant colonel who was involuntarily retired as a result of the Retirement Board's proceedings, filed in the Court of Federal Claims a class action complaint, seeking retroactive reinstatement and back pay. Count IV of his first amended complaint alleged that, "by imposing unlawful gender and racially classified retention goals . . . and selection consideration factors, and unlawful, gender and racially classified remedies for the possible disadvantages of societal discrimination," the Secretary and the Retirement Board "violated plaintiff's constitutional right to equal protection guaranteed under the Due Process Clause of the Fifth Amendment of the United States Constitution."

In its first opinion, the Court of Federal Claims granted summary judgment for Christian on his constitutional due process claim in Count IV. Christian, 46 Fed. Cl. at 815. The court held that the Secretary's instruction to the Retirement Board "created a race and gender-based goal and that it required consideration of different factors in evaluating minority and female officers than when evaluating white male officers," and that it therefore was subject to "strict scrutiny," "must serve a compelling governmental interest, and must be narrowly tailored to further that interest." Id. at 803 (citation omitted). The court concluded that the instructions did not meet those requirements, and that the "Army's affirmative action program for the 1992 [Retirement Board] . . . violates the Due Process Clause of the Fifth Amendment." Id. at 814.

The court also certified as the class for the action "the male nonminority officers selected by the [Retirement Board] for retirement." Id. at 816-17.

After further proceedings, the court issued a second opinion dealing with the remedy. Christian v. United States, 49 Fed. Cl. 720 (2001). It ruled that all members of the class were entitled to reinstatement as of the date of their initial illegal discharge and back pay and other remedies from that date to the date of their proper discharge. Id. at 722, 728. The court rejected the government's proposed "harmless error" analysis, under which the government proposed to establish a new selection board to determine which retired officers were harmed by the instructions, i.e., who would have been retained had the instructions not been given. Id. at 721. Instead, the court applied the "constructive service" doctrine, under which members of the military who have been improperly discharged are treated as having continued to serve until they are properly discharged; they are therefore entitled to back pay and allowances for that period of constructive service. Id. at 721-22. See, e.g., Tippett v. United States, 185 F.3d 1250, 1255 (Fed. Cir. 1999). The court held that Christian's retirement was both "involuntary" and "also legally improper, because the revote and the evaluation criteria in the [instructions] violated the equal protection component of the Fifth Amendment's Due Process Clause." 49 Fed. Cl. at 722.

The court certified the case for interlocutory appeal under 28 U.S.C. § 1292(d)(2) and this court authorized the government's appeal.

II

A. The doctrine of "harmless error" is a well-established settled principle of federal law. In the recent case of Texas v. Lesage, 528 U.S. 18, 120 S.Ct. 467, 145 L.Ed.2d 347 (1999), Lesage contended that the University of Texas, in denying him admission to a Ph.D. program, used a race-conscious admissions program in violation of the Equal Protection Clause of the Fourteenth Amendment. In seeking summary judgment, Texas "offer[ed] evidence that, even if the school's admissions process had been completely colorblind, Lesage would not have been admitted." Id. at 19, 120 S.Ct. 467. The district court granted summary judgment for Texas on this issue, but the Fifth Circuit reversed, viewing the question as "`whether the state violated Lesage's constitutional rights by rejecting his application in the course of operating a racially discriminatory admissions program.'" Id. at 20, 120 S.Ct. 467 (quoting Lesage v. Texas, 158 F.3d 213, 222 (5th Cir. 1998)). The Supreme Court summarily reversed. It stated:

Insofar as the Court of Appeals held that summary judgment was inappropriate on Lesage's § 1983 action seeking damages for the school's rejection of his application for the 1996-1997 academic year even if petitioners conclusively established that Lesage would have been rejected under a race-neutral policy, its decision is inconsistent with this Court's well-established framework for analyzing such claims. Under Mt. Healthy City Bd. of Ed. v. Doyle, 429 U.S. 274, 97 S.Ct. 568, 50 L.Ed.2d 471 (1977), even if the government has considered an impermissible criterion in making a decision adverse to the plaintiff, it can nonetheless defeat liability by demonstrating that it would have made the same decision absent the forbidden consideration. Our previous decisions on this point have typically involved alleged retaliation for protected First Amendment activity rather than racial discrimination, but that distinction is immaterial. The underlying principle is the same: The government can avoid liability by proving that it would have made the same decision without the impermissible motive.

Simply put, where a plaintiff challenges a discrete governmental decision as being based on an impermissible criterion and it is undisputed that the government would have made the same decision regardless, there is no cognizable injury warranting relief under § 1983.

. . . But where there is no allegation of an ongoing or imminent constitutional violation to support a claim for forward-looking relief, the government's conclusive demonstration that it would have made the same decision absent the alleged discrimination precludes any finding of liability.

Id. at 20-21, 120 S.Ct. 467 (citations omitted). Mt. Healthy involved a non-tenured schoolteacher who challenged the school board's refusal to rehire him. 429 U.S. at 274, 97 S.Ct. 568. He contended that the Board's decision was based on his exercise of free speech rights protected by the First and Fourteenth Amendments. Id. The Board contended that apart from the constitutionally protected activity, it would not have rehired him in any event. Id. at 285, 97 S.Ct. 568. The district court rejected the latter contention, and the court of appeals affirmed. Id. at 276, 97 S.Ct. 568. The Supreme Court vacated the court of appeals judgment and remanded. It stated:

Initially, in this case, the burden was properly placed upon respondent to show that his conduct was constitutionally protected, and that this conduct was a "substantial factor" — or to put it in other words, that it was a "motivating factor" in the Board's decision not to rehire him. Respondent having carried that burden, however, the District Court should have gone on to determine whether the Board had shown by a preponderance of the evidence that it would have reached the same decision as to respondent's re-employment even in the absence of the protected conduct.

Id. at 287, 97 S.Ct. 568 (footnote omitted).

As these cases indicate, the Supreme Court has recognized that a harmless error analysis is appropriate even for constitutional claims. "[T]he Court has applied harmless-error analysis to a wide range of errors and has recognized that most constitutional errors can be harmless." Arizona v. Fulminante, 499 U.S. 279, 306, 111 S.Ct. 1246, 113 L.Ed.2d 302 (1991) (citations omitted).

Indeed, the harmless error principle has been given statutory recognition in 28 U.S.C. § 2111 (2000), which provides:

§ 2111. Harmless error

On the hearing of any appeal or writ of certiorari in any case, the court shall give judgment after an examination of the record without regard to errors or defects which do not affect the substantial rights of the parties.

It also has been recognized in Rule 61 of the Federal Rules of Civil Procedure, and in Rule 52(a) of the Federal Rules of Criminal Procedure.

This court and its predecessor court have applied the harmless error analysis to military back pay cases. See Lindsay v. United States, 295 F.3d 1252, 1261 (Fed. Cir. 2002); Sanders v. United States, 219 Ct.Cl. 285, 594 F.2d 804 (1979); Skinner v. United States, 219 Ct.Cl. 322, 594 F.2d 824 (1979). "To recover back pay, it is not enough for the plaintiff to show merely that an error or injustice was committed in the administrative process; he must go further and either make a showing that the defect substantially affected the decision to separate him or relieve him from active duty, or at least he must set forth enough material to impel the court to direct a further inquiry into the nexus between the error or injustice and the adverse action." Hary v. United States, 223 Ct.Cl. 10, 618 F.2d 704, 707 (1980). If this burden is met, the "end-burden of persuasion falls to the Government to show harmlessness — that, despite the plaintiff's prima facie case, there was no substantial nexus or connection." Engels v. United States, 230 Ct.Cl. 465, 678 F.2d 173, 175 (Ct.Cl. 1982). But see the discussion in Part II D, below.

Under this authority, an officer cannot prevail in a challenge to a discharge after non-promotion if the government can demonstrate that, notwithstanding the error in the promotion proceedings, the officer still would not have been promoted. "[T]he quintessential military promotion question" is "whether it is unlikely that he . . . would have been promoted in any event." Porter v. United States, 163 F.3d 1304, 1318 (Fed. Cir. 1998) (citation and internal quotation marks omitted).

The present case is a classic instance for applying harmless error. The constitutional claim is that the white officers who were retired as a result of the Retirement Board proceedings were denied equal protection because of the instructions to the Board to give minority and female officers preferential treatment. The total number of minority and female officers retained was 341. Even if one were to assume that every one of those officers was retained solely because of an impermissible preference accorded minorities and females — a most unlikely assumption — at most that would mean that 341 white officers who were retired should have been retained.

The total number of white officers actually retired, however, who comprise the plaintiff class, was more than 1000. Thus, even under the most extreme assumption only about one-third of the white officers should have been retained. The Court of Federal Claims, however, would treat the entire group as having been improperly retired and give all of them reinstatement and back pay.

The present case fits comfortably within the Lesage standard. In Lesage the Court stated that "even if the government has considered an impermissible criterion in making a decision adverse to the plaintiff, it can nonetheless defeat liability by demonstrating that it would have made the same decision absent the forbidden consideration." 528 U.S. at 20-21, 120 S.Ct. 467 (citation omitted). In the present case the government has demonstrated with respect to at least two-thirds of the involuntarily retired male officers that it would have retired that number even without the impermissible instruction that favored minority and female officers.

"The general rule is that damages for breach of contract shall place the wronged party in as good a position as it would have been in, had the breaching party fully performed its obligation." Mass. Bay Transp. Auth. v. United States, 129 F.3d 1226, 1232 (Fed. Cir. 1997) (citations omitted). "A corollary of that principle is that the non-breaching party is `not entitled to be put in a better position by the recovery than if the [other party] had fully performed the contract.'" White v. Delta Constr. Int'l, Inc., 285 F.3d 1040, 1043 (Fed. Cir. 2002) (citation omitted). Applying those general rules of damages to the back pay claims in the present case, the applicable principle is that the retired white officers are entitled to be placed in the same position they would have been in if the Retirement Board had not considered the impermissible factors of race and gender in determining whom to recommend for involuntary early retirement, but not in a better position. Cf. Mt. Healthy, 429 U.S. at 285-86, 97 S.Ct. 568 ("[E]ven if the same decision would have been reached had the incident not occurred[,][t]he constitutional principle at stake is sufficiently vindicated if such an employee is placed in no worse a position than if he had not engaged in the conduct.").

The latter result, however, would follow from the Court of Federal Claims' denial of harmless error for two-thirds of the retired white officers. Although there is no theory upon which those officers would have been retained had there not been the inappropriate instruction to the Board, the effect of the court's decision is to treat them as if they had been all retained instead of retired. The harmless error doctrine is designed to prevent just such a result. We know of no reason, convincing or otherwise — and the Court of Federal Claims has not provided any — why this group of retired officers should receive such a substantial financial windfall representing back pay they could not and would not have received even if the Retirement Board proceedings had been wholly free from the taint the Court of Federal Claims found in them.

The amici contend that the government waived its harmless error claim by not asserting it sooner, and that the harmless error doctrine applies only to liability questions but not to damages issues. Since none of the parties has made or adopted either argument, we decline to consider them. In re Alappat, 33 F.3d 1526, 1536 (Fed. Cir. 1994) (citing United Parcel Serv., Inc. v. Mitchell, 451 U.S. 56 n. 2, 101 S.Ct. 1559, 67 L.Ed.2d 732 (1981) ("[A]micus may not rely on new arguments not presented below.")).

B. The Court of Federal Claims held, however, that "the relevant precedent in this case" is not Lesage, but the en banc Court of Claims decision in Doyle v. United States, 220 Ct.Cl. 285, 599 F.2d 984, as amended, 220 Ct.Cl. 326, 609 F.2d 990 (1979), cert. denied, 446 U.S. 982, 100 S.Ct. 2961, 64 L.Ed.2d 837 (1980). Christian, 49 Fed. Cl. at 724. Decisions of our predecessor courts are binding precedent in this court. South Corp. v. United States, 690 F.2d 1368, 1370 (Fed. Cir. 1982).

In Doyle, former Army Reserve officers challenged their release from active duty after they had been passed over twice for promotion by selection boards in 1974 and 1975. 599 F.2d at 988. At the time a statute required that Boards considering the promotion of reserve officers "`sh[ould] include an appropriate number of Reserves.'" Id. at 986 (citing 10 U.S.C. § 266(a) (1976)). Those selection boards had no reserve members.

When the error was discovered, the Secretary created new boards that had reserve members, and the reconstituted boards reconsidered all officers whom the original boards had considered. Id. at 991. "Although the reconstituted boards recommended promotion of some officers who were not selected by the original boards, none of the plaintiffs was among those recommended for promotion by either of the boards reconstituted for 1974 or 1975." Id. at 992.

The government conceded, and the Court of Claims held, that "the original 1974 and 1975 selection boards were improperly constituted because they did not include any Reserve officers as members." Id. The government contended, however, that since all the plaintiffs had again been passed over for promotion by the reconstituted selection boards which contained reserve officers, the lack of such officers on the original selection boards was harmless error because, even if those original boards had contained reserve members, they still would not have promoted the plaintiffs. Id.

The Court of Claims refused to apply the doctrine of harmless error. Noting that the "defective composition" of the original selection boards, id. at 993, was "directly related to the purpose and functioning of selection boards," id. at 994, and violated the reserve officers' "rights to fair procedure or process," the court concluded that "the doctrine of harmless error cannot be applied to this type of procedural error." Id. at. 996.

Doyle differs from the present case in two significant respects.

First, the "type of procedural error" in Doyle was the improper composition of the original Boards, whose membership violated a statutory requirement. The lack of reserve officers on those Boards deprived the plaintiffs of their statutory right to consideration by a tribunal containing officers of the same status they had. In the present case, on the other hand, the Retirement Board was properly constituted. The defect in the Board proceedings was the impermissible instructions given to the Board regarding preferential treatment of minority and female officers.

Second, in Doyle the result of the proceedings before the reconstituted boards was the basis upon which the government rested its claim of harmless error. In the present case, however, the government's harmless error claim rests upon the results of the original Board's proceedings. The government proposed to use the reconstituted board solely to determine the individuals with respect to whom the error was harmless.

Christian contends, however, that the government's proposed use of new retirement boards as a basis for applying the harmless error doctrine to the retired officers would involve an impermissible retroactive retirement of those officers whom the board would select, and that Doyle ruled that such action was improper. As just noted, however, the new retirement boards would be used for a different purpose in this case than the purpose for which they were used in Doyle. Indeed, it seems ironic that retired officers who will be reinstated and given back pay should complain that such action by the new retirement board would be improper.

Particularly in light of the Supreme Court's recent strong reaffirmation of the harmless error doctrine in Lesage, we decline to extend the Court of Claims' theory for rejecting harmless error in Doyle to the significantly different present case.

The Court of Federal Claims also relied on the decision of the District of Columbia Circuit in Dilley v. Alexander, 603 F.2d 914 (D.C. Cir. 1979), clarified by, 627 F.2d 407 (D.C. Cir. 1980). That was another case in which former Reserve officers challenged their release from active duty after they had been twice been passed over for promotion by Boards that did not have Reserve members. 603 F.2d at 916. The District of Columbia Circuit, like the Court of Claims in Doyle, held that the absence of Reserve members on the Board was a fatal flaw in the administrative proceedings. Id.

As in Doyle, the Army contended that the subsequent pass overs by new promotion boards that had Reserve members "demonstrate that the defect in the composition of the 1975 Boards did not result in any prejudice to appellants." Id. at 921. The court rejected that argument because "the prejudice which the statute guaranteed against, insofar as reserve officers were concerned, was consideration by a promotion board devoid of reserve officers." Id. Although the court did not use the phrase "harmless error" in discussing the issue, that was the concept it considered and rejected.

The decision of the District of Columbia Circuit in Dilley does not bind this court. For the reasons given in our discussion of Doyle, we do not consider Dilley a persuasive precedent for the present case.

C. The Court of Federal Claims also invoked the constructive service doctrine as a ground for rejecting the harmless error claim in this case. Under that doctrine, military personnel who have been illegally or improperly separated from service are deemed to have continued in active service until their legal separation. Clackum v. United States, 148 Ct.Cl. 404, 296 F.2d 226, 229 (1961). They are, therefore, entitled to back pay and benefits for the intervening period, i.e., retroactive to their original separation from service. Egan v. United States, 141 Ct.Cl. 1, 158 F.Supp. 377, 386 (1958). Hary, 618 F.2d at 707. As the District of Columbia Circuit stated in its clarifying opinion in Dilley, the constructive service doctrine is a "legal fiction": "as appellants have never been lawfully terminated from active duty, they are deemed to have served during the time of their illegal release." 627 F.2d at 413. To recover back pay under the doctrine, the former service person must have been improperly separated from the service and there must be a "nexus between the error . . . and the adverse action." Hary, 618 F.2d at 707.

Nothing in the constructive service doctrine is inconsistent with applying harmless error in this case. The constructive service doctrine was designed to permit the award of back pay to a service person who had been injured by the improper termination of his service, and thereby denied the financial and other benefits he should and would have received but for the improper termination. In the present case, the retired white officers who would have been retired even if the impermissible instruction had not been given to the Retirement Board cannot be properly viewed as having had their military service improperly terminated, and they therefore have not been injured. There is, accordingly, no occasion to invoke the constructive service doctrine for them, since they have no claim, legal or equitable, to back pay for any period during which they did not perform military duty. Indeed, as we have noted above, both this court and the Court of Claims have applied the harmless error principle in military back pay cases.

D. The year after the Doyle decision, there was a significant "change in law governing the review of twice passed-over officers." Porter v. United States, 163 F.3d 1304, 1323 (Fed. Cir. 1998). The Defense Officer Personnel Management Act in 1980 included what is now 10 U.S.C. § 628 (2000), which authorizes the Secretary of the military service involved to appoint a special selection board "to make promotion or passover decisions when original selection boards had passed over an officer in circumstances in which the officer's record before the original boards contained faulty OERs [officer effectiveness reports]." Porter, 163 F.3d at 1313. In Porter, this court considered the effect of section 628 upon the harmless error doctrine in cases in which military officers who had been discharged as a result of being twice passed over for promotion by promotion boards challenged those passovers as based upon service records that contained serious errors. Id. at 1321-24. This court ruled:

The harmless error test, while necessary to adjudicate cases such as this before the enactment of section 628, is not only unnecessary now, but grafting it onto section 628 is sufficiently problematic for us to reject that possibility. In cases such as this, the harmless error rule has no application.

Id. at 1324.

In our subsequent decision in Richey v. United States, 322 F.3d 1317 (Fed. Cir. 2003), we explained that

In Porter we held that once it is determined that the initial selection board's decision "involved material administrative error," nothing in this statute requires the Secretary, acting through the Corrections Board, to make a harmless error determination. Instead, under the statute, as interpreted in Porter, the Corrections Board should refer the matter to an SSB [special selection board], which decides whether to promote the officer based on his corrected military record, and, therefore, "the harmless error rule has no application."

Id. at 1324 (citing Porter, 163 F.3d at 1323).

In the context before the court, the statement in Porter that the harmless error rule is inapplicable "[i]n cases such as this" refers to cases that section 628 covers, i.e., those in which an officer twice passed over for promotion by a promotion board challenged his ensuing discharge as based on alleged errors in his service records before that board. Porter concluded that prior decisions of the Court of Claims and this court that had applied harmless error in that situation had been overruled "because of the change in law" made by section 628, namely, the Secretary's authority to refer such a case to a special selection board to decide whether the officer should be promoted. 163 F.3d at 1323-24.

Neither Porter nor Richey is inconsistent with our application of harmless error in the present case. This case involves officers released from active duty pursuant to the recommendation of a retirement board, whose task was to reduce the total number of officers of the same rank on active duty. It does not involve officers discharged as a result of having been twice passed over for promotion. At the time this case was decided, section 628 covered only the latter type of case, but not the former. (In 2001 Congress enacted 10 U.S.C.A. § 1558 (1998 Supp. 2003), which provided for retirement boards a similar procedure to that section 628 provides for promotion boards. As the government recognizes, however, that new provision does not apply to the present case.)

Indeed, the administrative inquiry in those cases was significantly different from the inquiry in the present case. In the passover discharge cases, there were two questions: (1) was the officer's service record (on which the promotion board based its decision) incorrect and, if so, (2) would the officer have been promoted on a proper record. Porter and Richey ruled that since section 628 substituted for the second inquiry a re-evaluation of the officer by a special selection board on the basis of a proper service record, there was no need or occasion for a harmless error analysis.

In the present case, however, two propositions are already established: (1) the original retirement board proceedings were tainted by the improper instructions and (2) under no circumstances could approximately two-thirds of the white officers who were retired have been retained if there had not been the improper instructions. Although a harmless error inquiry was neither necessary nor appropriate in the passover discharge cases because of section 628, without such an analysis in the present case approximately two-thirds of the white retired officers would receive a substantial financial windfall to which they have no valid claim.

III

The government urges, as it did in the Court of Federal Claims, that if we accept its argument on harmless error, the case should be remanded for the Secretary to appoint a new Retirement Board, which would evaluate anew the officers the Retirement Board considered in 1992 and, without the impermissible instructions, make new recommendations for retention and release. The Secretary then would determine which white male officers who were released should and would have been retained. We agree that the case should be remanded, but we think the Secretary should be able to follow an alternative procedure if he deems it appropriate.

At oral argument, the government stated that the "order of merit" list for the officers the Retirement Board considered no longer existed and that it was uncertain whether the officers' ranking could be determined from other data. We do not know whether the available information would permit the Secretary, without appointing a new retirement board, to determine which of the retired officers would have been retired even had there been no impermissible instructions to the Retirement Board regarding minority and female officers. What is clear, however, is that (1) at most, approximately one-third of the plaintiffs would be entitled to recover, because that equals the maximum total number of minority and female officers retained, and (2) since the additional minority officers retained in phase 2 were so treated to eliminate the disparity between the non-retention rate for minority officers and that for all officers, without the impermissible instructions no additional white male officers would have been retained in lieu of those additional minority officers kept on duty.

The Secretary might conclude that instead of appointing a new retirement board that would reevaluate all the officers involved, he can determine, and therefore should designate for reinstatement and back pay, those retired white male officers who, had there not been the impermissible instruction, would have been retained. We do not know whether the Secretary would have sufficient information to be able to make such determination.

We indicate no view on what would be the most appropriate procedure for the Secretary to follow. That is a matter that lies preliminarily within his informed discretion. Our discussion of this point was merely intended to suggest to the Secretary a possible alternative approach for determining which members of the plaintiff class are entitled to relief. Of course, the Secretary may conclude that the available information does not enable him to make such determination and that a new retirement board is necessary.

Once the Secretary determines which members of the plaintiff class are entitled to reinstatement and back pay, the case will be returned to the Court of Federal Claims to consider any challenges to the Secretary's decision and to formulate an appropriate judgment.

CONCLUSION

The decision and order of the Court of Federal Claims is reversed insofar as it refused to apply harmless error in this case, and the case is remanded to that court with instructions to remand the case to the Secretary for further proceedings consistent with this opinion.

REVERSED IN PART AND REMANDED.