The present invention relates to a cosmetic composition, in particular a hair composition, comprising i) one or more dicarbonyl compounds corresponding to formula (I) below, and/or derivatives thereof and/or hydrates thereof and/or salts thereof: in which formula (I): R represents an atom or group chosen from i) hydrogen, ii) carboxyl &mdash；C(O)OH, iii) linear or branched C1-C6 alkyl which is optionally substituted, preferably with at least one hydroxyl &mdash；OH radical, carboxyl &mdash；C(O)&mdash；OH radical or halogen such as Br, iv) optionally substituted phenyl, v) optionally substituted benzyl, iv) and v) preferably being optionally substituted with at least one &mdash；OH or &mdash；C(O)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, and ii) at least one amino silicone, the composition having a pH of less than or equal to 4, and also to a process for straightening the hair using this composition.
