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In the paper, ldquoImproved Transmission Scheme for Orthogonal Space Time Codesrdquo, a new scheme is proposed that uses an iterative Expectation Maximization (EM) algorithm for decoding and provides full rate and full diversity. For full rate, some of the codeword symbols are not transmitted but rather estimated at the receiver using the expectation maximization (EM) algorithm. In this paper, we prove analytically that the EM algorithm converges exponentially and unconditionally to the least squares (LS) estimate and the rate of convergence depends on the channel parameters and not on the initial vector. We also propose a new very low complexity decoding for the aforementioned transmission scheme with identical error performance.