An adaptive LMS filtering system is proposed for computing the Discrete Walsh Transform (DWT). The signal to be transformed serves as the `desired signal' for the adaptive filter, while a set of periodic Walsh sequences serve as the input signal vector for the adaptive filter. The weights of the adaptive filter provide the DWT. The given approach is more efficient in terms of the required computations and memory locations compared with the direct approach. In contrast with existing Fast DWT algorithm, the proposed solution provides more flexibility as far as the signal block length is concerned. In other words, the proposed approach is not restricted to a block length N to be of power 2.