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A recursive asymptotic impedance matrix method is presented for simple and stable analysis of electromagnetic waves in bianisotropic media. The method overcomes the numerical instability problem associated with the transition matrix method. It requires only elementary matrix operations along with thin-layer asymptotic approximation and bypasses the intricacies of the eigenvalue-eigenvector approach. Exploitation of its self-recursion algorithm with geometric subdivision of a layer leads to high computation efficiency. The method also facilitates the trade-off between accuracy and speed for various applications.