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This paper proposes two novel non-orthogonal space-time block coding schemes with code rates of 2 and 1.5 complex symbols per channel use for four and three transmit antennas. The proposed coding scheme with rate-2 is designed by four Alamouti codes. In order to reduce the decoding complexity effectively, the simplified maximum likelihood algorithm is adopted at the receiver. From the point of view of the channel capacity, for the cases of one and more than one receive antennas, the proposed code is with excellent performance. The BER simulation results prove that the proposed coding scheme is with better performance at lower SNR.