A pulverulent composition for bleaching human keratin fibers, and more particularly the hair, comprising at least one peroxygenated salt, at least one polymer chosen from nonionic and anionic amphiphilic polymers, wherein said at least one polymer comprises at least one fatty chain; and at least one polydecene of formula C10nH[(20n)+2] in which n ranges from 3 to 9, the at least one polydecene being present in an amount by weight of less than 10% relative to the total weight of the composition. The pulverulent composition is capable of being mixed with at least one aqueous hydrogen peroxide composition having a titre of not more than 40 volumes to form stable, homogeneous, bleaching compositions that can be applied precisely and easily, and can produce a homogeneous bleaching of the hair that does not leave the hair coarse.