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This paper describes another computational algorithm for the discrete Fourier transform(DFT) via the discrete Walsh transform(DWT). The number of multiplications required by this algorithm is approximately NL/9 where N is the number of data points and L is the number of Fourier coefficients desired. This number shows a 33 % decrease against NL/6 in the previous algorithm published by us. The proposed algorithm can be derived by using conventional sampling points in the DFT. The DFT computation via the DWT is superior to the fast Fourier transform(FFT) approach in applications where L is relatively small compared with N and where the Walsh and Fourier coefficients are both desired.