A process for the bleaching of chemical pulp, wherein the initial bleaching of the pulp includes a first chlorine dioxide treatment (D0) and a following alkaline treatment with oxygen and hydrogen peroxide (EOP), which stages are separated from each other with a washing stage, and a treatment of the pulp to reduce the content of transition metals of the pulp prior to the peroxide treatment. The process is characterized in that alkali is added to the pulp after addition of chlorine dioxide in the D0 stage to adjust the pH of the pulp to neutral or basic (N stage) prior to the washing stage following the chlorine dioxide stage, whereby the initial bleaching includes the sequence D0N EOP.