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Generalized Zero Forcing (GZF) is an extension of the zero forcing beamforming method to deal with downlink multiuser MIMO communications when users have more than one receive antenna. In literature, Singular Value Decomposition (SVD) based channel Block Diagonalization (BD) is proposed to eliminate multiuser interference for GZF, but it is computationally inefficient. In this letter, we propose to generate a GZF precoder by using the product of a channel pseudo inverse matrix and a block diagonal matrix with an appropriate form, whose optimality for solving weighted sum rate maximization and weighted sum power minimization problems is proven. Later by using the proposed precoder a novel BD method with significantly lower complexity is presented. The complexity analysis shows that our proposal is computationally more efficient than SVD-BD.