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Recently, space-time block codes (STBC) with a partial interference cancellation (PIC) group decoding was proposed to deal with the tradeoff among rate, diversity and complexity by Guo and Xia. In this paper, we propose a systematic design of STBC with reduced-complexity PIC group decoding. The proposed STBC is featured as Alamouti-type block code in which each entry of Alamouti code matrix is replaced by a block of multi-layer coded symbols. With the PIC group decoding and a particular grouping scheme, the proposed STBC can achieve full diversity, rate- 2M/M+2 and a low-complexity decoding for M transmit antennas. Simulation results show that the proposed codes can achieve the full diversity with PIC group decoding while requiring half decoding complexity of the existing codes.