Several quasi-orthogonal STBCs (QOSTBCs) designs using four transmit antennas have been proposed. However, these STBC codes do not maintain full diversity due to the limitations of their complex orthogonal design. In this paper, we propose a code selection method with single-phase feedback which eliminates most of the interference by selecting the QOSTBC with less interference from among two predefined QOSTBCs. The BER performance improvement is investigated in relation with the single-phase feedback scheme at the expense of one bit.