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Paraunitary matrices play an important role in the design of perfect reconstruction filter banks. There are building blocks that generate the whole family of both FIR and IIR one-dimensional paraunitary matrices over the complex field. Because of applications in digital signal and image processing, there has been an attempt to generalize the factorization methods to the two-dimensional case. However, no general building block that covers all two-dimensional IIR paraunitary matrices has been found yet. In this paper, we present a factorization for two families of such matrices.