In this paper, a generalized pruning procedure on the input of radix-2 DIF FHT algorithm is presented. For situations in which relative number of zero-valued samples is quite large, a systematic pruning procedure can be introduced on the input of the FHT algorithms, thereby reducing the amount of computational complexity. The novelty of this procedure is that the exact number of non-zero samples is taken into consideration, instead of approximating them to the nearest higher 2-power integer.