The present invention relates to a cosmetic composition comprising at least one cationic polymer and/or one amphoteric polymer and at least 3% of one or more dicarbonyl compounds corresponding to formula (I) below 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 or formula (A). 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.
