The present invention relates to a cosmetic composition comprisingone or more dicarbonyl compound corresponding to formula (I) below thereof and/or hydrates thereof and/or salts thereof:in which formula (I) R═H, COOH, linear or branched C1-C6 alkyl optionally substituted with an OH or COOH or Br radical； phenyl or benzyl optionally substituted with an OH or COOH radical； or alternatively an indolyl radical orwith * representing the part linked to the rest of the molecule, the dicarbonyl compounds corresponding to formula (I) 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 preferably solid fatty substances, the non liquid 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.The invention also relates to a process for straightening keratin fibres, especially the hair, which comprises the application to the hair of the composition of the invention, followed by a straightening step using a straightening iron at a temperature of at least 150° C., preferably ranging from 150 to 250° C.
