The peptide group connecting Tyr440 and Ser441 of the bovine cytochrome c oxidase is involved in a recently proposed proton-transfer path (H-path) where, at variance with other pathways (D- and K-paths), a usual hydrogen-bond network is interrupted, thus making this proton propagation rather unconventional. Our density-functional based molecular dynamics simulations show that, despite this anomaly and provided that a proton can reach a nearby water, a multistep proton-transfer pathway can become a viable pathway for such a reaction: a proton is initially transferred to the carbonyl oxygen of a keto form of the Tyr440-Ser441 peptide group [-CO-NH-], producing an imidic acid [-C(OH)-NH-] as a metastable state; the amide proton of the imidic acid is then transferred, spontaneously to the deprotonated carboxyl group of the Asp51 side chain, leading to the formation of an enol form [-C(OH)=N-] of the Tyr440-Ser441 peptide group. Then a subsequent enol-to-keto tautomerization occurs via a double proton-transfer path realized in the two adjacent Tyr440-Ser441 and Ser441-Asp442 peptide groups. An analysis of this multistep proton-transfer pathway shows that each elementary process occurs through the shortest distance, no permanent conformational changes are induced, thus preserving the X-ray crystal structure, and the reaction path is characterized by a reasonable activation barrier.