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This paper investigates the cancellation of the interfereences among Destination Users (DU's) and the improvement of system rate in the non- regenerative Multiuser Multiple-Input Multiple- Output (MU-MIMO) relay downlink system. A novel design method of transmit weights is proposed to successively eliminate the interference among DU's, each of which is equipped with multiple receive antennas. We firstly study the transmit weights design for the conventional Amplify-and-Forward (AF) relay system where the Relay Station (RS) just retransmits the received signals, then we extend it to the joint design of transmit weights both at the Base Station (BS) and the RS. In the joint design, Singular Value Decomposition (SVD) is used for the first channel link (link between BS and RS), then a user selection algorithm is adopted at the RS to generate the transmit weight of each DU. The channel matrix of system is transformed into a triangular matrix, where the Dirty Paper Coding (DPC) technique is employed to remove the interference among DU's and maintain the achievable rate of system. Simulation results verify the effectiveness of the proposed scheme.