In this paper, we study the impact of spatial correlation on the performance of Unitary space time codes (USTC). We derived the exact expression and upper bound on the Pair-wise error probability (PEP) for USTC over quasi-static Rayleigh flat fading channel when Generalize likelihood ratio test (GLRT) decoder is employed. This bound, which has a closed form expression, is more tight and simpler than other existing bound. In addition, we establish a theorem that the spatial correlation has no impact on the diversity gain, whereas it merely reduces the coding gain and thereby degrades the performance curve. Simulation results confirm the theoretical analysis.