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The exact pair-wise error probabilities (PEP) formulas developed for space-time (S-T) coding so far either are not in the closed forms or have the closed forms but need to calculate very complicated high order derivatives, and so are not easy to use. This paper derives, for S-T coding in block Rayleigh fading, a new exact PEP formula which is expressed as the summation of a series of terms to the powers of 1/signal-to-noise-ratio (1/SNR). The result gives researchers an easier and more convenient way for bit-error-rate (BER) evaluation and optimization of S-T coded multiple-input-multiple-output (MIMO) systems. Monte Carlo simulation results of the BER performance of a 2-by-2 S-T coded system are used to verify our results.