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In this letter, we propose a quasi-orthogonal spacetime block coding (QO-STBC) scheme with maximum likelihood (ML) decoding via simple linear detection. A conventional QOSTBC scheme can achieve the full rate, but at the cost of decoding complexity and diversity gain. These disadvantages of the conventional QO-STBC scheme are mainly a result of interference terms in the detection matrix. In this letter, we propose a new QO-STBC scheme which eliminates interference terms. The proposed method achieves improved diversity gain with respect to the conventional QO-STBC scheme, as well as a great reduction in decoding complexity.