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A full rate space-time block code (STBC) for four transmit antennas based on quasi-orthogonal design is proposed in this paper. The 4times4 transmission matrix of the presented quasi-orthogonal space-time block code (QOSTBC) is constructed based on Alamouti's scheme. The original maximum-likelihood (ML) decoding scheme and the low-complexity ML (LC-ML) decoding scheme for the new code are introduced. Then the decoding speed of them is compared. The simulation results show: the performance of the new code is better than that of orthogonal space-time block codes (OSTBC) at low SNR; it also exceeds the bit error rate (BER) of OSTBC at high SNR if the new code uses constellation rotation; the LC-ML decoding scheme is faster than the original ML decoding scheme.