This paper introduces a new efficient design scheme for spatial multiplexing (SM) systems over closed loop multiple-input multiple-output (MIMO) wireless channels. Extending the orthogonalized spatial multiplexing (OSM) scheme which was developed recently for transmitting two data streams, we propose a new SM scheme where a larger number of data streams can be supported. To achieve this goal, we partition the data streams into several subblocks and execute the block-diagonalization process at the receiver. The proposed scheme still guarantees single-symbol maximum likelihood (ML) detection with small feedback information. Simulation results verify that the proposed scheme achieves a huge performance gain at a bit error rate (BER) of 10-4 over conventional closed-loop schemes based on minimum mean-square error (MSE) or bit error rate (BER) criterion. We also show that an additional 2.5dB gain can be obtained by optimizing the group selection with extra feedback information.