An efficient procedure for the design of finite length impulse response filters with linear phase is presented. The algorithm obtains the optimum Chebyshev approximation on separate intervals corresponding to pass and/or stop bands, and is capable of designing very long filters. This approach allows the exact specification of arbitrary band-edge frequencies as opposed to previous algorithms which could not directly control pass and stop band locations and could only obtain N-1 / 2 different band edge locations for a length N low-pass filter, for fixed phi1 and phi2. As an aid in practical application of the algorithm, several graphs are included to show relations among the parameters of filter length, transition width, band-edge frequencies, passband ripple, and stopband attenuation.