The correlations of Walsh functions are defined and some of their properties derived. One property proved is a recursion relation, which relates correlations of high index functions to those of low index functions. Successive.applications of the equations yield an expression for evaluating the correlations at a restricted value of the time shift. From this expression we then find some matrix recursion relations that can be used to rapidly evaluate $2^n \times 2^n $ values of cyclic or noncyclic correlations at any time shift.