Cosmetic use of one or more catalytic oxidation compounds chosen from porphyrin compounds of following formula: in which: R 2, R 3, R 5, R 6, R 8, R 9, R 11 and R 12, which are identical or different, represent a hydrogen atom; a linear or branched C 1 -C 30 alkyl radical, which can be interrupted by one or more heteroatoms and/or which can be substituted; a linear or branched C 2 -C 30 alkenyl radical, which can be interrupted by one or more heteroatoms and/or which can be substituted; or a linear or branched C 2 -C 30 alkynyl radical, which can be interrupted by one or more heteroatoms and/or which can be substituted; R 2 and R 3, R 5 and R 6, R 8 and R 9 and/or R 11 and R 12 can respectively form, with the carbon atoms carrying them, an optionally substituted aryl ring, preferably a phenyl ring; R 1, R 4, R 7 and R 10, which are identical or different, represent a cationic group, such as optionally substituted pyridinium; an anionic group, such as phenyl substituted by a sulfonate SO 3 - group; a linear or branched C 8 -C 30 alkyl radical, which can be interrupted by one or more heteroatoms and/or which can be substituted; or a reactive group, which can be chosen from siloxanes, esters and compounds comprising one or more thiol groups; M corresponds to a metal or a metal ion chosen from transition metals and metals from Group IIA, in particular Mg, Group IIB, in particular Zn, and possibly Groups IB to VIIB, in particular Mn, of the Periodic Table of the Elements; p has the value 0 or 1; in particular, p has the value 1, to catalyse the oxidation of the bacteria responsible for the decomposition of human sweat into volatile compounds producing unpleasant body odours. R 2, R 3, R 5, R 6, R 8, R 9, R 11 and R 12, which are identical or different, represent a hydrogen atom; a linear or branched C 1 -C 30 alkyl radical, which can be interrupted by one or more heteroatoms and/or which can be substituted; a linear or branched C 2 -C 30 alkenyl radical, which can be interrupted by one or more heteroatoms and/or which can be substituted; or a linear or branched C 2 -C 30 alkynyl radical, which can be interrupted by one or more heteroatoms and/or which can be substituted; R 2 and R 3, R 5 and R 6, R 8 and R 9 and/or R 11 and R 12 can respectively form, with the carbon atoms carrying them, an optionally substituted aryl ring, preferably a phenyl ring; R 1, R 4, R 7 and R 10, which are identical or different, represent a cationic group, such as optionally substituted pyridinium; an anionic group, such as phenyl substituted by a sulfonate SO 3 - group; a linear or branched C 8 -C 30 alkyl radical, which can be interrupted by one or more heteroatoms and/or which can be substituted; or a reactive group, which can be chosen from siloxanes, esters and compounds comprising one or more thiol groups; M corresponds to a metal or a metal ion chosen from transition metals and metals from Group IIA, in particular Mg, Group IIB, in particular Zn, and possibly Groups IB to VIIB, in particular Mn, of the Periodic Table of the Elements; p has the value 0 or 1; in particular, p has the value 1, to catalyse the oxidation of the bacteria responsible for the decomposition of human sweat into volatile compounds producing unpleasant body odours.