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In this paper, we present a new design method of infinite impulse response (IIR) digital filters with quasi-equiripple absolute error in the complex domain. This method is based on solving a least squares solution iteratively. At each iteration, the desired response for the least squares approximation is transformed to have equiripple error. This algorithm is efficient because there is no need for any initial value or complex optimization algorithm. By this method, a quasi-equiripple solution is obtained very quickly with less computational complexity. Moreover, by multiplying an arbitrary weighting function on the desired responses of passband and stopband, respectively, the error at the passband and stopband can be controlled. Finally, we show some examples to validate the proposed method.