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We present a complex, full-rate quasi-orthogonal space-time block code for four transmit antennas. Using carefully tailored constellation phase rotations, we show that this code achieves full diversity for specialized PSK-based constellations. The optimal receiver for the new code decouples the symbol detection problem into pairs of symbols, thus greatly reducing complexity. Finally, we present and compare performance of the new code with several other codes in the literature. The new code is shown to perform as well as the best known code of its class.