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This paper presents a new method to approximate an IIR filter with a FIR filter so that the obtained FIR filter has the same magnitude and group delay as the original IIR filter. This method is formulate as minimization of an error transfer function between the given IIR filter and the desired FIR filter which is designed using the mean least square error (MLSE) technique. Analyzing of this method shows that this method converges to an accurate approximation when places of the IIR filter poles in Z-plane are in an elliptic with radiuses equal to 0.4 and 0.14 in imaginary and real axis, respectively. Several examples are presented in order to show this method efficiency.