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In this paper a method is described to compute the group delay of a minimum phase network from the attenuation characteristic via Hilbert transformation and spline function. The passband distortion due to dissipative loss can also be obtained with minimum amount of computation. The new approach eliminates all the numerical problems encountered in earlier attempts by many authors. As a result of its accuracy, the method can be profitably applied to assist the design of filters. An example is given to show the application and the numerical results of the method.