to 6 by weight more particularly from 2 to 4 by weight relative to the weight of dry mechanical pulp the alkaline agent may be selected from alkaline metal and alkaline earth metal oxides hydroxides silicates and carbonates ammonia aqueous ammonia and mixtures thereof the preferred basic species for selection of the alkaline agent including potassium hydroxide sodium hydroxide magnesium hydroxide calcium hydroxide sodium carbonate sodium silicate magnesium carbonate and mixtures thereof sodium hydroxide potassium hydroxide or a mixture thereof is particularly preferred the alkaline agent of the bleaching composition preferably comprises sodium silicate sodium silicate has an auxiliary function of stabilizing the bleaching agent especially the hydrogen peroxide in the bleaching composition it is also possible to provide another stabilizing agent in addition to or instead of the sodium silicate polyhydroxyacrylate compounds constitute possible stabilizing agents the amount of alkaline agent used is preferably from 0 5 to 10 by weight preferably from 1 to 6 by weight preferably from 1 4 to 4 by weight more particularly from 1 6 to 2 5 by weight relative to the weight of dry mechanical pulp the bleaching composition may further comprise a chelating agent as defined above especially if the chelating step is not carried out or ended at incomplete chelation it should be noted that the bleaching composition may be prepared separately and then contacted with the mechanical pulp but it may also be prepared directly in contact with the mechanical pulp in this second case the various compounds of the bleaching composition are added successively and directly to the mechanical pulp the duration of.