AbstractThis paper proposes a direct design method in the z‐domain for the IIR digital filter with a parallel structure composed of allpass networks with complex and real coefficients, with the specifications for the bandedge frequencies of the passband and stopband as well as the magnitude in the passband (or stopband).First, a filter composed of two allpass networks with conjugate complex coefficients is considered. Also, the phase difference characteristic between the two networks is considered. By specifying the phase difference error, the determination of the filter coefficients is reduced to the eigenvalue problem of the matrix using Remez' algorithm. The filter coefficients are determined from the eigenvector corresponding to the maximum eigenvalue. Then iterative calculation is executed to realize the equiripple characteristic, and the optimal solution is derived.Next, the relation between the phase difference errors and the magnitude errors is discussed and it is shown that the filter can be designed by the proposed method by specifying the absolute value of the magnitude error. The usefulness of the proposed method is shown by design examples. The filter based on two allpass networks with real coefficients is also considered, and it is shown that the filter can be designed by the same procedure by formulating the procedure for the sum and the difference of the filter coefficients.