High-yield lignocellulosic wood pulps are bleached by (i) first pretreating such pulp with a complexing agent for metal ions and next washing the pretreated pulp, and then (ii) bleaching such pretreated/washed pulp with an initial amount of hydrogen peroxide in an alkaline medium, including adding a supplementary bleaching amount of hydrogen peroxide and a supplementary amount of an alkaline agent to the pulp over the course of the bleaching step (ii) without interrupting same, at a point in time when from 60% to 85% of the initial amount of hydrogen peroxide has been consumed, and such supplementary amount of hydrogen peroxide being equal to or less than the initial amount thereof.