Cosmetic composition comprising - one or more dicarbonyl compounds corresponding to formula below and/or hydrates thereof and/or salts thereof: in which formula: R represents an atom or group chosen from i) hydrogen, ii) carboxyl -C OH, iii) linear or branched C 1 -C 6 alkyl which is optionally substituted, preferably with at least one hydroxyl -OH radical, carboxyl -C -OH radical or halogen radical such as Br; iv) optionally substituted phenyl, v) optionally substituted benzyl, iv) and v) preferably being optionally substituted with at least one -OH or -C OH radical; vi) an indolyl radical and vii) an imidazolylmethyl radical and tautomers thereof such as with * representing the part linked to the rest of the molecule, the dicarbonyl compounds corresponding to formula and/or hydrates thereof and/or salts thereof being present in an amount ranging from 3 to 15% by weight relative to the total weight of the composition, - one or more cationic surfactants, - one or more non liquid and preferably solid fatty substances, the non liquid and preferably solid fatty substances being present in an amount ranging from 1% to 30% by weight relative to the total weight of the composition, the composition having a pH of less than or equal to 4. - one or more dicarbonyl compounds corresponding to formula below and/or hydrates thereof and/or salts thereof: in which formula: R represents an atom or group chosen from i) hydrogen, ii) carboxyl -C OH, iii) linear or branched C 1 -C 6 alkyl which is optionally substituted, preferably with at least one hydroxyl -OH radical, carboxyl -C -OH radical or halogen radical such as Br; iv) optionally substituted phenyl, v) optionally substituted benzyl, iv) and v) preferably being optionally substituted with at least one -OH or -C OH radical; vi) an indolyl radical and vii) an imidazolylmethyl radical and tautomers thereof such as with * representing the part linked to the rest of the molecule, the dicarbonyl compounds corresponding to formula and/or hydrates thereof and/or salts thereof being present in an amount ranging from 3 to 15% by weight relative to the total weight of the composition, R represents an atom or group chosen from i) hydrogen, ii) carboxyl -C OH, iii) linear or branched C 1 -C 6 alkyl which is optionally substituted, preferably with at least one hydroxyl -OH radical, carboxyl -C -OH radical or halogen radical such as Br; iv) optionally substituted phenyl, v) optionally substituted benzyl, iv) and v) preferably being optionally substituted with at least one -OH or -C OH radical; vi) an indolyl radical and vii) an imidazolylmethyl radical and tautomers thereof such as with * representing the part linked to the rest of the molecule, the dicarbonyl compounds corresponding to formula and/or hydrates thereof and/or salts thereof being present in an amount ranging from 3 to 15% by weight relative to the total weight of the composition, - one or more cationic surfactants, - one or more non liquid and preferably solid fatty substances, the non liquid and preferably solid fatty substances being present in an amount ranging from 1% to 30% by weight relative to the total weight of the composition, the composition having a pH of less than or equal to 4.