The invention relates to a process for the bleaching of chemical pulp, wherein the pulp is delignified and/or bleached with chlorine dioxide or with a combination of chlorine dioxide and a per-compound, and additionally the pulp is chelated in order to bind heavy metals, such as Fe, Mn and/or Cu, to a chelate complex. The chelate complex is selected from the group made up of N-bis-[(1,2-dicarboxylethoxy)-ethyl]-amine, N-bis[(1,2-dicarboxylethoxy)-ethyl]-aspartic acid and N-tris-[(1,2-dicarboxylethoxy)-ethyl]-amine, and the alkali metal and earth-alkali metal salts of these, and the chelating treatments are carried out simultaneously by combining the chelating chemical with the pulp in the same bleaching stage as chlorine dioxide.