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Orthogonal space-time block codes (OSTBC) are powerful codes that provide high performance at low decoder complexity. The systematically designed half-rate OSTBCs by Tarokh et al, make a particularly important class of these codes because they can be systematically constructed for an arbitrary number of transmit antennas. In this paper, we propose a new formulation of the maximum likelihood (ML) decoder for general OSTBCs, and use the specific structure of the above half-rate OSTBCs to reduce the number of computations for their ML decoder. When the product of the number of transmitters and the receivers is much larger than the constellation size, this method reduces the number of computations by a factor of two. This reduction of the number of computations is achieved while maintaining the optimality of the decoder.