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An algorithm for computing the QR decomposition of a polynomial matrix is introduced. The algorithm proceeds to perform the decomposition by following the same strategy in eliminating entries of the matrix as is used in the Givens method for a QR decomposition of a scalar matrix, however polynomial Givens rotations are now required. A possible application of the decomposition is in MIMO communications, where it is often required to reconstruct data sequences that have been distorted due to the effects of co-channel interference and multipath propagation, leading to intersymbol interference. If the channel matrix for the system is known, its QR decomposition can be calculated and used to transform the MIMO channel equalisation problem into a set of single channel problems, which can then be solved using a maximum likelihood sequence estimator. Some simulated average bit error rate results are presented to support the potential application to MIMO channel equalisation.