The present invention relates to a cosmetic composition comprising:one or more dicarbonyl compounds corresponding to formula (I) below, and/or derivatives thereof and/or hydrates thereof and/or salts thereof:one or more amine-generating derivatives chosen from the compounds of formula (II) below, salts thereof, tautomers thereof or hydrates thereof:The invention also relates to a process for straightening keratin fibers, 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.
