A new Space-Time Block Code (STBC) achieving full rate and full diversity for general QAM and four transmit antennas is proposed. This code also possesses a quasi-orthogonal (QO) property like the conventional Minimum Decoding Complexity QO-STBC (MDC-QO-STBC), leadingg to joint ML detection of only two real symbols. The proposed code is shown to exhibit the identical error performance with the existing MDC-QO-STBC. However, the proposed code has an advantage in transceiver implementation since this code can be modified so that the increase of PAPR occurs on only two transmit antennas, whereas MDC-QO-STBC incurs a PAPR increase on all transmit antennas.