A method for systematically constructing Fast Walsh Transform algorithms is given，This method is applicable to binary-ordered Walsh-，Paley-，Sequency-ordered Walsh-Kaczmarz-and Kronecker-ordered Walsh-Hadamard Transformations.Using this method，some FWT algorithms already known from literature can be presented in a novel way by means of certain matrix factorizations，As the transformations are normally done with the aid of a digital computer，it is important to establish effective and time-saving computer algorithms.