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In MIMO communication systems, performance analysis is very important for the comparison of different transmit schemes. In this paper, we consider three widely used modulations and use the moment generation function (MGF) approach and the Gauss- Chebyshev integration to present an efficient numerical computation method for the symbol error rate (SER) of orthogonal space-time block codes (OSTBC) over correlated MIMO channels. Our work can greatly reduce the complexity for evaluating SER and provide valuable insights into the performance of OSTBC. Finally, computer simulation results demonstrate that the new method is correct and effective.