A process for delignification and bleaching of a chemically digested lignocellulose-containing pulp, wherein the pulp is bleached at a pH in the range from about 1 up to about 6 with a bleaching chemical selected from the group consisting of chlorine dioxide, ozone, peracetic acid and acid peroxides, whereupon a water-soluble chemical containing magnesium is added at a pH in the range from about 1 up to about 7 and in an amount of from about 0.01 up to about 10 kg/ton of dry pulp, calculated as magnesium, and that subsequently the pulp is bleached with hydrogen peroxide at a pH of from about 8 up to about 12.