A method of moving a receiving window in a wireless mobile communication system, wherein the AM RLC of the transmitting side sends information of the last discarded SDU regardless of continuity of the discarded SDUs. The AM RLC of the receiving side checks whether all SDUs from the start point of the receiving window up to the last discarded SDU are successfully received, delivers the SDUs that are successfully received to an upper layer, and discard only those SDUs that are not successfully received.