A water-free composition for the bleaching and brightening of human hair at the same time with a simultaneous conditioning effect is disclosed. The particularly exceptional effects of the bleaching agent is that improvement of shine and elasticity. The bleaching agent comprisesa) at least one compound with a bleaching or brightening effect, in particular a peroxide and/or an ammonium salt, andb) 0.001% to 10% by weight, calculated to the total composition, of at least one ubiquinone of the formula (I)