The present invention relates to a cosmetic composition comprising:one or more dicarbonyl derivatives corresponding to formula (I) below, 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 which is optionally substituted with an OH or COOH or Br radical； phenyl or benzyl optionally substituted with an OH or COOH radical； or alternatively an indolyl radical orone or more silanes corresponding to formula (II) below and/or oligomers thereof:R1Si(OR2)z(R3)x(OH)y (II)in which formula (II):R1 is a linear or branched, saturated or unsaturated, cyclic or acyclic C1-C6 hydrocarbon-based chain substituted with a group chosen from the following groups: amine NH2 or NHR (R=C1-C20 and especially 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 unsubstituted or substituted, in particular with an amino group or with a C1-C4 aminoalkyl group； R1 possibly being interrupted with a heteroatom (O, S or NH) or a carbonyl group (CO),R2 and R3, which may be identical or different, represent a linear or branched alkyl group comprising from 1 to 6 carbon atoms,y denotes an integer ranging from 0 to 3, andz denotes an integer ranging from 0 to 3, andx denotes an integer ranging from 0 to 2,with z+x+y=3.The invention also relates to a process for straightening keratin fibers, especially the hair, using the compounds of formulae (I) and (II) with a straightening step using a straightening iron at a temperature of at least 150° C., preferably ranging from 150 to 250° C.
