The present invention relates to a cosmetic composition comprising – one or more dicarbonyl derivatives corresponding to the following formula (I) and/or derivatives thereof 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 which are optionally substituted with an OH or COOH radical； or else an indolyl radical of formula (III), - one or more silanes corresponding to the following formula (II) and/or oligomers thereof: in which formula (II): R1 is a C1-C6 hydrocarbon-based chain which is linear or branched, saturated or unsaturated, cyclic or acyclic, and substituted with a group chosen from the groups: - amine NH2 or NHR (R = C1-C20, in particular C1-C6, alkyl optionally substituted with a radical comprising a silicon atom, C3-C40 cycloalkyl or C6-C30 aromatic), - or with a hydroxyl group, - a thiol group, - an aryl or aryloxy group which is substituted or unsubstituted, in particular with an amino group or with a C1-C4 aminoalkyl group； it being possible for R1 to be interrupted with a heteroatom (O, S, NH) or a carbonyl group (CO), R2 and R3, which may be identical or different, are a linear or branched alkyl group comprising from 1 to 6 carbon atoms, y denotes an integer ranging from 0 to 3, and z denotes an integer ranging from 0 to 3, and x denotes an integer ranging from 0 to 2, with z + x + y = 3. The subject matter of the invention is also a method for straightening keratin fibres, in particular the hair, using the compounds of formulae (I) and (II) with a straightening step by means of a straightening iron at a temperature of at least 150°C, preferably ranging from 150 to 250°C.La présente invention concerne une composition cosmétique comprenant -un ou de plusieurs dérivés dicarbonylés répondant à la formule (I) suivante et/ou leurs dérivéset/ou leurs hydrateset/ou leurs sels: formule (I) dans laquelle R = H, COOH,
