A systematic and in -depth research on the construction of Walsh function are carried out. The formula of constructing continuous Walsh function with Rademacher function is improved. A complete set of mutually transforming methods between the numbers of the discrete Walsh function and the row or rank numbers of Hadamard matrix is brought up and their relationship is put in order, thus building up a unified and corresponding relationship between the discrete Walsh function which is made from the row or rank of Hadamard matrix and the continuous Walsh function and constructing the discrete Walsh function, with the way of sampling, by continuous Walsh function.