In this paper, we propose a new spatial multiplexing scheme for transmission over flat-fading multiple-input multiple-output (MIMO) channels, which allows a simple maximum-likelihood decoding at the receiver with small feedback information. We begin with a real-valued representation of the complex-valued system model and show that we can achieve orthogonality between transmitted signals by applying a proper rotation to transmitted symbols. Based on the minimum Euclidean distance between received vectors, we also present a simple antenna selection metric for the proposed spatial multiplexing systems. Simulation results demonstrate that our spatial multiplexing system performs close to the optimum closed loop system with much reduced complexity and feedback overhead.