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Recently several STBC designs were proposed for MIMO systems with linear receivers. In this paper, we propose a new design of high-rate STBC with linear receivers. Compared to the overlapped Alamouti code (OAC) recently proposed by Shang and Xia, the new STBC has a higher symbol rate without guarantee of achieving full diversity. To achieve the same rate, the new STBC has only a half of the block length (code delay) of the OAC. Simulation results show that in comparison with some existing codes for a given rate the proposed STBC can give a better outage probability performance.