The present invention relates to a composition comprising: at least one dicarbonyl compound of formula (I) below and/or derivatives thereof and/or hydrates thereof and/or the corresponding salts: in which formula (I): R represents an atom or group chosen from i) hydrogen, ii) carboxyl &mdashC(O)OH, iii) optionally substituted linear or branched C1-C6 alkyl, iv) optionally substituted phenyl, v) optionally substituted benzyl, vi) an indolyl radical, and vii) an imidazolylmethyl radical, and tautomers thereof, at least one cellulose-based polymer and at least one amphoteric surfactant, the composition having a pH of less than or equal to 4. The invention also relates to a process for straightening keratin fibers such as 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 between 150 and 250° C.
