The invention is related to a method for the preparation of kraft pulp with increased pulping yield from lignin-containing cellulosic material using polysulfide cooking liquor. In order to obtain a cost efficient system both in aspects of investment costs but also in aspects of heat economy of operating the process is most of the total charge of alkali charged as heated polysulfide liquor to an first atmospheric vessel, wherein the hot polysulfide liquor flashes off steam providing most if not all of the necessary steaming effect for the cellulose material. The polysulfide liquor is then allowed to impregnate the cellulose material at a temperature closer to cooking temperature but still so low that essentially no delignification occurs in impregnation vessel, as the H-factor in impregnation vessel is kept within 1-20.