Block Diagonalization (BD) algorithm is a generalization of channel inversion scheme in multiuser multi-input multi-output (MIMO) broadcast channels. Although the BD algorithm is effective in removing interuser interference, it has a drawback that additional information should be delivered to the receiver. Recent work on BD with vector perturbation (VP) avoids the need for additional information and hence reduces receiver complexity. In this paper, we propose a method achieving further gain in the BD for multiuser MIMO downlink. By combining the BD and minimum mean square error vector precoding (MMSEVP), we pursue the balance between the interference suppression and the noise enhancement control, resulting in considerable improvement in the effective SINR. In fact, simulation results on the realistic multiuser downlink scenario show that the proposed method brings substantial performance gain over existing multiuser MIMO algorithms (BD, BD-VP and BD-WF).