An algorithm has been developed for calculating sequency-ordered fast Walsh-Fourier transforms (FWT's) using an additive recursion formula. Sequency-ordered FWT's of an N-dimensioned sampled data set are generated by a summation recursion of FWT's on subintervals of the data set. The algorithm is fast (N log2 N summations), computer efficient, and can be applied to time-dependent spectral analysis of nonstationary phenomena such as speech.