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It is well known that a complex orthogonal design that provides full diversity and full transmission rate exists only for two antennas. For larger number antennas either the symbol rate or full diversity needs to be sacrificed in general. In this paper, we present a quasi-orthogonal space time block code (QOSTBC)for four transmit antennas based on group precoding (GP), which we call GP-QOSTBC, that achieves full rate and full diversity. The optimal receiver for the new code decouples the symbol detection problem into pairs of symbols, thus greatly reducing decoding complexity. Simulation results show that the proposed quasi-orthogonal code outperforms the previous Jafarkhani code and coordinate-interleaved space-time block codes.