Unitary space-time code is ideally suited for rapid fading scenarios as it can operate well without channel state information (CSI), which is of vital significance for improving the effectivity and reliability of wireless communication systems. Pair-wise error probability (PEP) is an important factor for studying the reliability of a communication system. However, the existing scheme only gives the final result of PEP and the corresponding Chernoff upper bound (CUB) is obtained through magnification, which is not of universal significance for this kind of problems. In this paper, we employ the log-likelihood ratio of probability density functions of the received signals conditioned on the two possibly transmitted signals and by virtue of moment generating function we give the details in deriving the final precise residue expression for PEP and its CUB. At last, we verify the above results by simulations. Unitary space-time code is ideally suited for rapid fading scenarios as it can operate well without channel state information (CSI), which is of vital significance for improving the effectivity and reliability of wireless communication systems. Pair-wise error probability (PEP) is However, the existing scheme only gives the final result of PEP and the corresponding Chernoff bound (CUB) is obtained through magnification, which is not universal relevance for this kind of problem. In this paper, we employ the log-likelihood ratio of probability density functions of the received signal conditioned on the two potentially transmitted signals and by virtue of moment of moment function we give the details in deriving the final precise residue expression for PEP and its CUB. At last, we verify the above results by simulations.