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Through appropriate formulation of a step in the factorization algorithm of an elementary paraconjugate Hermitian polynomial matrix, the exponential time bound for this step is reduced to a low-order polynomial. As the remaining steps have a bound of the same type, considerable time-saving is entailed in larger problems. The procedure utilizes the fact that the relevant matrix may be viewed as the incidence matrix of a bipartite graph. The reduction involves finding the strongly connected components of the graph, resulting from the solution of an assignment problem.