Process for preparing polyether polyols having an end block of ethylene oxide by addition of alkylene oxides onto H-functional starter substances, in which A) a polyether polyol precursor is prepared by means of double metal cyanide (DMC) catalysis in a semicontinuous mode of operation in which previously prepared polyether polyol together with the DMC catalyst are placed in a reactor and H-functional starter substance and propylene oxide are added continuously, B) the polyether polyol precursor from stage A) is reacted with propylene oxide or an ethylene oxide/propylene oxide mixture in the presence of the DMC catalyst in a continuously operating reactor to give a polyether polyol intermediate, C) the intermediate from stage B) is mixed with an alkali metal hydroxide as catalyst and D) reacted with ethylene oxide in a continuously operating reactor to give the final product, E) the catalyst is separated off from the final product obtained in stage D).