In this paper, we present a novel maximum likelihood (ML) decoding algorithm for space-time block codes (STBC) over fading channels. Using a lattice representation for space-time codes by transforming complex channel models into real matrix equations, we propose a new efficient ML decoding algorithm with performance identical to the conventional ML decoder. We show that the complex orthogonal space-time codes, in fact, allow a separate ML decoding for each in-phase and quadrature-phase component. For rate one quasi-orthogonal designs with N transmit antennas (N ≥ 4), the proposed decoding scheme reduces the decoding complexity from script O sign (M cN/2) to script O sign(McN/4) in a Mc-QAM constellation. Moreover, multidimensional rotated constellations are constructed by which the quasi-orthogonal codes can achieve full diversity, while the proposed ML decoding method offers significant computational savings as compared with previous approaches.