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In this work we present a semi-blind algorithm for the estimation of a flat-fading MIMO channel matrix H. The algorithm is based on a decomposition of the channel matrix H as the product of a whitening matrix W and a unitary matrix Q. The whitening matrix can be estimated blindly from all received data. Several techniques are then suggested to estimate the optimum rotation matrix from training samples. Since it uses both blind and training data, the algorithm is semi-blind in nature. Theoretical results show that estimation of the channel matrix based on estimating only the Q matrix from pilot data can perform more efficiently than estimating H directly from the pilot data. However, performance of the technique depends on the accuracy with which W is estimated and is found to typically perform well in low SNR and fading environments.