Abstract: The method is for bleaching cellulose pulp in a bleach line that has at least two bleaching steps. The filtrate distribution is led up through the bleaching line counter-currently to the flow of cellulose pulp established in the bleaching line. A single joint main conduit is used for the bleaching steps. Wash filtrates obtained from the wash steps, used after or before the bleaching step, are led in conduits to branch locations on the main conduit that are positioned downstream of the branch location for drawing off of wash and/or dilution liquor for the wash step in question. All branch points in the joint main conduit are in fluid communication with one another along the main conduit.