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The decoding of space-time orthogonal block (STOB) codes that have been proposed recently to achieve a diversity gain proportional to multiplication of the number of transmit and receive antennas is studied. We present a matrix formulation for such decoders. This formulation is found useful for efficient implementation of decoders and facilitate analysis. As examples, we use the new formulation to study the correlation property of the noise samples and derive a formula for signal-to-noise ratio at the space-time decoder output.