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In this paper, we propose a new coordinated spatial multiplexing algorithm for multiuser multiple-input multiple-output (MIMO) downlink systems. Unlike other conventional coordination methods, our scheme exploits orthogonalized effective channels to yield the transmit precoding and receive combining matrices without requiring an iterative operation. In order to determine each row of the effective channels, a greedy type successive process is utilized. Simulation results show that the performance of our proposed scheme is very close to the conventional iterative scheme with significantly reduced complexity. Also, our method achieves a 3 dB performance gain over the conventional non-iterative scheme.