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A new method is proposed for designing of two-channel filter banks (FBs) with causal-stable IIR filters having an approximate cosine-rolloff (CR) transition band. By using IIR filters with a CR transition band, the flatness condition required for two-channel NPR FB is automatically satisfied. The design problem of IIR FBs is reduced to the design of FIR fliers if we can propose locating the poles of IIR filters. Then the design problem can be formulated as a convex minimax optimization problem, and solved by second order core programming (SOCP). Moreover, tie polyphase components of tie analysis Alters are assumed to have an identical denominator in order to simplify the PR condition. The two-channel NPR IIR FB so obtained has a reasonably low reconstruction error and it can be employed as the initial guess to constrained nonlinear optimization software for designing the PR IIR FB.