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Space-time block coding (STBC) has been proposed to achieve transmit diversity in wireless communication systems. Most works on STBC system assume the availability of perfect channel state information (CSI) at the receiver. Also assume that the antennas are well separated so that the received signals are uncorrelated. However, in practice, the CSI is not always known at the receiver and the received signals are sometimes correlated. In this paper, a computationally efficient channel estimation scheme is presented for STBC system under spatially correlated Rayleigh fading channel. A decorrelation algorithm is introduced to decorrelate the correlated received signals before this computationally efficient channel estimator is used. Some simulation results are presented to demonstrate the performance of proposed channel estimator in STBC system under spatially correlated Rayleigh fading channel.