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 comprises a) at least one compound with a bleaching or brightening effect, in particular a peroxide and/or an ammonium salt, and b) 0.001% to 10% by weight, calculated to the total composition, of at least one ubiquinone of the formula (I) ##STR00001## wherein n is a number from 1 to 10, and at least one sphingolipid of the formula II ##STR00002## where R.sup.1 and R.sup.2 are independent from each other alkyl- or alkenyl group mit 10 to 22 carbon atoms, R.sup.3 is methyl, ethyl, n-propyl or isopropyl group and n is a number between 1 to 6, preferably 2 or 3.