This letter deals with computationally efficient maximum-likelihood (ML) detection for the quasi-orthogonal space-time block code (QOSTBC) with four transmit antennas. The proposed ML detector uses a permutation based real-valued equivalent channel matrix representation. As a result, the complexity of ML detection problem is moderated from O(2 vertical bar A vertical bar(2)) to O(4 vertical bar A vertical bar), where vertical bar A vertical bar is modulation order. Numerical results show that the proposed ML detector provides ML performance and achieves greatly high computational savings.