The present invention relates to a non-dyeing composition comprising: (i) one or more cationic acrylic copolymers comprising at least the units obtained from the following monomers: a) monomer derived from acrylic or methacrylic esters or amides and comprising at least one cationic group, and b) alkyl acrylate or methacrylate monomer, the alkyl radical comprising from 1 to 30 carbon atoms, preferably 1 to 22 carbon atoms, better still 1 to 10 carbon atoms and preferentially 2 to 6 carbon atoms. and (ii) one or more conditioning agents chosen from functionalized silicones, cationic polymers and cationic surfactants, and mixtures thereof.