The present disclosure relates to a cosmetic agent for bleaching human hair, comprising (i) a package comprising at least one multi-layer film, which comprises at least one metal-containing layer as a barrier layer, and (ii) a bleaching agent composition, which is contained in the package, wherein the bleaching agent composition contains at least one percarbonate, at least one inorganic salt of a peroxysulfuric acid, and at least one thickener. The present disclosure also relates to a method for bleaching human hair.