Bleaching of laundry using a peroxidized compound is carried out at a temperature of less than 70.degree. C. for less than 30 minutes in a bath which has a pH of 10.5 to 12.5 in the presence of 1.times.10.sup.-3 to 1.times.10.sup.-2 gram-atom of calcium or of barium per liter of bath and of a sequestrant for alkaline earth metal ions in a quantity equal or superior to that which corresponds to the sequestration of calcium or barium ions in solution in the bath; the calcium or the barium being introduced in the form of the oxide CaO or BaO; the hydroxide Ca(OH).sub.2 or Ba(OH).sub.2 ; or of a salt, the anion of which is inert towards hydrogen peroxide and which is accompanied by a quantity of sodium hydroxide equal to that required for the formation of calcium hydroxide or barium hydroxide.