Disclosed herein is an anhydrous paste for bleaching human keratin fibers, such as hair, comprising at least one peroxygenated salt, at least one alkaline agent, from 15% to 35% by weight of at least one polydecene of formula C10nH[(20n)+2] wherein n ranges from 3 to 9, such as from 3 to 7, relative to the total weight of the paste, and from 0.01% to 10% by weight of at least one gelling agent chosen from hydrophilic fumed silicas, hydrophobic fumed silicas and diblock, triblock, multiblock and radial-block copolymer comprising at least one segment of styrene monomers and at least one segment of monomers chosen from thermoplastic monomers and comonomers, relative to the total weight of the paste.