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The existence of finite-length one-step linear predictors plays a key role in several existing algorithms for blind identification and equalization of multiple-input multiple-output (MIMO) systems. An upper bound on the length of the predictor is known for the case when the underlying MIMO transfer function is irreducible and column-reduced. When the MIMO transfer function is irreducible but not necessarily column-reduced, it is known that a finite-length linear predictor exists; however, its length has not been specified in the literature. An upper bound on the length of a linear predictor for MIMO systems with irreducible transfer functions is derived.