Cosmetic composition, process for smoothing keratin fibers and use of the composition The present invention relates to a cosmetic composition comprising - one or more dicarbonyl compounds corresponding to formula (i) below, their hydrates and their salts: wherein in the formula (i) r = h, cooh, C1-C6 straight or branched alkyl optionally substituted with an oh, cooh or br radical； phenyl or benzyl optionally substituted with an oh or cooh radical； or alternatively an indolyl radical or with * representing the moiety attached to the rest of the molecule, the dicarbonyl compounds corresponding to formula (i) ei or their hydrates ei or their salts being present in an amount ranging from 3 to 15% by weight by weight. relative to the total weight of the composition, - one or more cationic surfactants, - one or more non-liquid substances, preferably solid, fatty, 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 4.2. The invention also relates to a process for straightening keratin fibers, in particular hair, comprising applying 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.composição cosmética, processo para alisamento das fibras de queratina e uso da composição a presente invenção refere-se a uma composição cosmética compreendendo - um ou mais compostos de dicarbonila correspondentes à fórmula (i) abaixo, seus hidratos e i ou seus sais: em que na fórmula (i) r = h, cooh, c 1 -c 6 alquila linear ou ramificado opcionalmente substituído com um radical oh, cooh ou br； fenila ou benzila opcionalmente substituído com um radical oh ou cooh； ou alternativamente um radical indolila ou com * representando a parte ligada ao resto da molécula, os compostos de dicarbonila correspondendo à
