In [1], the authors have proposed one high rate transmission scheme for Space-Time Block Codes (STBC) without additional system source such as power, bandwidth and time slot. To maintain the full rank property of the coding gain matrix, we propose a set of STBCs for 4 transmit antennas transmission to transmit one additional information bit achieving rate-9/8. Another orthogonal STBC code with rate-1 is proposed in this paper within the set. It shows by computer simulation results that by employing the set of STBCs, it achieves better bit error rate (BER) performance and throughput than that of [1] with a valid BER improvement at the high SNR region above 20dB.