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Original proposal of cooperative extended balanced space-time block coding (CEBSTBC) and its special subsets like cooperative balanced space-time block coding (CBSTBC) utilize all available relays to guarantee full diversity and to maximize the coding gain when a few bits of feedback from the destination to the relays are available. Due to the construction technique of the CEBSTBC, one of the channel gains does not contribute the coding gain. In addition, since all relays transmit equal power, contribution of a minimum path gain does not yield high signal-to-noise ratio at the destination. To maximize received signal-tonoise ratio at the destination with a limited feedback, a novel transmit scheme for the CEBSTBC is proposed. This scheme transmits only N-1 out of N relays and a relay which maximize the received signal-to-noise ratio at the destination doubles its transmit power. The proposed scheme improves performance of the CEBSTBC and its subsets and outperforms path selection and relay selection schemes. Another advantage of the proposed scheme is allowing minimum decoding delay for the CEBSTBC and its subsets.