The invention relates to a cosmetic composition which is intended, in particular, for bleaching human keratin fibers, particularly hair, which have been dyed with oxidation dyes and/or direct dyes. The inventive composition comprises sulphunic acid derivatives having general formula (I) in a cosmetically-acceptable medium, at a pH of between 1.5 and 9. The invention also relates to novel compounds having formula (I), the devices comprising several compartments which are used to dye and bleach the aforementioned fibers and the bleaching method using said composition