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This paper proposes a modified frequency response masking (FRM) technique for the synthesis of linear phase, sharp transition, low arithmetic complexity FlR filter. The structure is composed of lowpass and bandpass subfilters which are designed as linear phase, equiripple passband and computationally efficient FIR filters. The frequency response of the subfilters are modeled using trigonometric functions of frequency and the design yields closed form expressions for the impulse response coefficients of the subfilters. The slopes at the edges of the transition region of the subfilter are matched which makes the frequency response a continuous function of frequency and hence reduces the effects due to Gibb's phenomenon thereby reducing passband edge ripple of the subfilters. The bandpass filter eliminates one masking filter and a model filter from the basic FRM approach thereby simplifying the synthesis of the proposed modified FRM FIR filter.