For unitary space-time code (USTC), the impact of spatial correlation on error performance is investigated. A tighter and simpler upper bound is derived for generalized likelihood ratio test decoder. We establish that the spatial correlation does not change the diversity gain, whereas it degrades the error performance of USTC. Motivated by the precoding of space-time block code, we designed a precoder for USTC to handle the case of the joint transmit-receive correlation. Numerical results show that the degradation in performance due to spatial correlation can be considerably compensated by the proposed algorithm.