This paper proposes a new precoding algorithm for orthogonalized spatial multiplexing (OSM) systems over flat-fading multiple-input multiple-output (MIMO) channels. The OSM scheme was recently introduced for closed-loop MIMO systems which allows single symbol decodability for maximum likelihood detection. To further improve the performance in OSM systems, we propose a new precoding method. For identifying the parameters of a precoder, we introduce a partitioning approach on the minimum Euclidean distance between constellation points in the effective channel. Also, it is shown that two real value parameters and one bit are required for feedback information in 4-QAM systems. Simulation results demonstrate that our precoding algorithm allows us to significantly improve the system performance with small increase of feedback values. We also confirm through simulations that the performance of the proposed scheme is the same as the optimum closed-loop MIMO systems.