A hair bleaching process reduces hair damage to bleached hair and comprises the steps of (i) preparing an aqueous bleaching composition by mixing three compositions (a), (b) and (c), wherein the composition (a) is a substantially anhydrous composition comprising at least one compound with bleaching effect, the composition (b) is an aqueous composition comprising at least one oxidizing agent, and the composition (c) comprises at least one compound selected from the group consisting of water soluble silk protein, water soluble silk protein hydrolysate and of derivatives of water soluble silk protein and water soluble silk protein hydrolysate, (ii) reducing cysteic acid content and formation in bleached hair by applying the aqueous bleaching composition onto hair and (iii), after processing of 5 to 45 min at a temperature in the range of 20 to 45° C., rinsing the aqueous bleaching composition off from the hair.
