In multiuser MIMO systems, block diagonalization (BD) eliminates inter-user interference with perfect CSI since the transmitter decomposes a multiuser MIMO channel into multiple parallel independent single-user MIMO channels. For a large number of users, the transmitter selects a subset of users who have good channels to maximize the system throughput. In this paper, a new low complexity scheduling algorithm with BD is proposed since an exhaustive search for the optimal user set is impractical. Simulation results show that the proposed algorithm has much lower complexity while it achieves the total throughput close to the optimal algorithm. It also has lower complexity than previous low complexity scheduling algorithms.