Recently, some attempts have been made to apply stochastic computation to realization of Finite Impulse Response (FIR) digital filters. Such new FIR filter realizations lead to significant reduction of hardware complexity over the conventional filter realizations based on binary computation. However, the stochastic FIR filters suffer from lower computational accuracy than the FIR filters based on binary computation. This paper presents a new method for realization of stochastic FIR filters to improve computational accuracy. In the proposed method, multipliers are realized using stochastic computation but adders are realized using binary computation. Evaluation results demonstrate that our method achieves a 7dB improvement in stopband attenuation.