A multicomponent packaging unit for reductive decolouration of colored keratin fibers, which comprises, presented separately from one another, a container (A) containing a cosmetic agent (a) and a container (B) containing a cosmetic agent (b); wherein the agent (a) in container (A) contains one or more sulfinic acid derivatives from a group as defined in claim 1, one or more fatty constituents from the group consisting of fatty alcohols, fatty acid triglycerides, fatty acid monoglycerides, fatty acid diglycerides, fatty acid esters, hydrocarbons and/or silicone oils, and has a water content of at most 10.0wt%, based on the total weight of the agent (a); and wherein the agent (b) in container (B) has a water content of at least 30.0wt%, based on the total weight of the agent (b). Preferably the sulfinic acid derivative is formamidinesulfinic acid and the fatty constituent is liquid paraffin. Agent (a) is preferably anhydrous. Agent (b) may also comprise alkalizing agents, such as ammonia, alkanolamines or amino acids and preferably has a basic pH of 7.5-12.5. Also disclosed is a method for reductive decolouration of colored keratin fibers using the multicomponent packaging unit, comprising preparing a ready-to-use decolouring agent by mixing cosmetic agents (a) and (b).