A process for the production of bleached pulp which comprises subjecting unbleached pulp obtained by digesting a lignocellulosic material to oxygen-alkali bleaching and then elementary-chlorine-free bleaching involving chlorine dioxide treatment, wherein peroxomonosulfuric acid is jointly used in at least one of the stages of chlorine dioxide treatment to reduce the amount of chlorine dioxide used and to improve the discoloration resistance of bleached pulp.