N.M. Stat. § 77-8-12
The cancellation of an existing mark or brand of a sheep owner shall in no way affect a lien on or interest in any sheep claimed by a third person, and as to such third person a cancellation shall not be deemed to have taken place. Where a new or different brand is awarded the owner, such interested third person or lien holder may have the instrument on which he bases his lien amended so as to show the date the new mark or brand was awarded, a description or facsimile of such new mark or brand and the sheep affected by such new mark or brand. Such amended instrument must be signed and acknowledged in the same manner as the original instrument to give it the force and effect of the original instrument, and recorded, where required by law, in order to give constructive notice.
NMS § 77-8-12