Recently an orthogonalized spatial multiplexing scheme with optimal precoding, referred to as POSM, has been proposed. The POSM achieves optimal performance in terms of maximizing the received minimum Euclidean distance dmin, R in closed-loop multiple-input multiple-output (MIMO) systems. In this paper, we derive exact closed-form expressions of the symbol error rate (SER) for the POSM with 4-QAM and 16-QAM in Rayleigh fading channels. We first introduce a new system model for the given channel. Based on this system model and a unique feature of the POSM effective constellations, the final expression of the SER using polar coordinates can be evaluated with a single-integral form. Simulation results confirm the accuracy of our derived analysis.