Abstract: A low complexity block diagonalization precoding algorithm is proposed for multiuser multiple-input multiple-output (MIMO) downlink systems. It is proved that the algorithm can achieve the same sum capacity with that of the traditional block diagonalization one. The algorithm improves the existing zero forcing method. By performing Gram-Schmidt orthogonalization to zero forcing beams, the algorithm can achieve fast global block diagonalization of the equivalent downlink channel, thus further obtaining the precoders. Avoiding matrix singular value decomposition required when calculating null space in the traditional block diagonalization algorithm, the computational complexity of the proposed algorithm is greatly reduced by about 50%.