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 —C(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 andat 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.
