In this letter, we present a new decoder for quasi-orthogonal space-time block code (QOSTBC) based on conditional maximum-likelihood (ML) decoder. The proposed decoder results in the decoding complexity of $\mathcal {O}(L^{1})$ , where $L$ is the constellation size. In addition, by decomposing the real and imaginary components of the received signals, we further reduce the complexity of the decoder. Unlike many of previous decoders proposed for QOSTBC, our decoder is compatible with any complex-valued constellation such as quadrature amplitude modulation. Furthermore, the advantage of the proposed decoder with respect to other decoders is analyzed in terms of preprocessing and detection complexity. The simulation results show the identical bit error rate performance of the proposed and conventional ML decoder.