The invention relates to an agent for changing the color of keratinous fibers, in particular human hair. In a cosmetic carrier, such agents contain at least one coloring component and at least one cationizable copolymer that is not permanently ionic. Said copolymer is derived from at least one cationizable monomer of the general formula (F1), where R1 and R2 independently of each other represent hydrogen or a methyl group, R3 and R4 independently of each other represent alkyl groups having 1 to 4 carbon atoms, Y represents an NH group or an oxygen atom, and p represents an integral number between 2 and 5. Said agents can be obtained, in particular, by mixing the individual components of a multiple-component packaging unit, wherein oxidation dye precursor products and direct-dyeing colorants can be used as coloring agents. The invention further relates to a method for applying such agents on keratinous fibers. Moreover, the invention relates to the use of said agent for improving color retention.