In this correspondence we show the existence of a Reed-Muller like expansion for multivalued functions. We establish that any m-variable, N-valued function [mi]f(xm,xm-1,...x1[/mi]) can be expressed as [mi]Co+ C1x1+ *--+ + CNm_1xmN-1xm-1N-1x1N-1[/mi]. A matrix method for determining the coefficients of these expansions is presented. The problem of finding minimal expression for a given function is discussed. Finally, we present a new technique for realizing multiple output functions.