Multiuser (MU) - multiple input multiple output (MIMO) techniques were proposed to increase the spectrum efficiency because only a few antenna branches are allowed at a simple mobile terminal (MT). Among the MU-MIMO techniques, the block diagonalization (BD) algorithm is well known as a practical linear precoding technique for a downlink. In this paper, we analyze an achievable bit rate in MU-MIMO using BD algorithm and derive the simplified expression using the signal spaces of users. Based on the derived expression, two kinds of user selection methods for the BD algorithm (USBD) in MUMIMO systems are proposed. The proposed methods estimate the improvement in the achievable bit rate compared to that in a single user (SU)-MIMO system using the signal spaces of the supported users. The first proposed method is USBD with a full search (USBD-FS) and it selects the combination of users to achieve the highest total throughput by considering all the combinations. The second proposed method is USBD with a tree structure search (USBD-TS), which drastically reduces the calculation complexity. Although all combinations of users are not considered in USBD-TS, a sufficient achievable bit rate is obtained while the calculation load is much less than that for the conventional method. Computer simulations confirm that USBD-FS and USBD-TS obtain the achievable bit rate of 100.0% and 91.1% compared to that for the best combination of users when the angle spread at the transmitter is 75°.