Proton transfer between protonated formohydroxamic acid (FAH)(+) and water molecules (H2O-FAH-H2O)(+) is studied theoretically. In a proton-relay mechanism, the carbonyl oxygen in formohydroxamic acid (HCONHOH, FA) accepts a proton from the hydronium ion (H3O+) and releases a proton either from the amine group (N-H) or the N-hydroxyl (N-OH) of formohydroxamic acid to another H2O molecule. The movement of the two protons is not simultaneous but through a stepwise process. The catalytic effect of the H2O molecule in reducing the proton-transfer barrier compared to the catalytic effect of pure formohydroxamic acid through intramolecular proton transfer is substantial. The transfer barriers of the two protons in a relay process are asymmetric. The proton on either the amine group (N-H) or the N-hydroxyl (N-OH) of FAH(+) will be transferred to the second H2O molecule, and the proton transfer is determined by the lengths R-N . . .O and R-O . . .O, which are related to the distance between FAH(+) and the second H2O molecule. At the same R-N . . .O and R-O . . .O, the proton on amino group (N-H) has a transfer energy barrier lower than that of the proton on the N-hydroxyl site by about 4.1 kcal/mol. If we elongate the distance between the two water molecules and let protonated FA shuttle freely as a proton carrier between the two water molecules, then the energy barrier for the movement of protonated FA increases slowly with the increase of the distance between two H2O's separated by no more than 10 Angstrom. However, the proton-transfer barrier between protonated FA and water is independent of the separated distance of the two water molecules.