In this paper, using diagonal signal repetition with Alamouti code employed as building blocks, we propose a high-rate groupwise space-time block code (GSTBC) which can be effectively decoded by a low-complexity successive interference cancellation (SIC) based receiver. The proposed GSTBC and SIC based receiver are jointly designed such that the diversity repetition in a GSTBC can induce the dimension expansion to suppress interfering signals as well as to obtain diversity gain. Our proposed scheme can be easily applied to the case of large number of antennas while keeping a reasonably low complexity at the receiver. It is found that the required minimum number of receive antennas is only two for the SIC based receiver to avoid the error floor in performance. The simulation results show that the proposed GSTBC with SIC based receiver obtains a near maximum likelihood (ML) performance while having a significant performance gain over other codes equipped with linear decoders.