In this paper we describe a new representation of p-adic functions, the so-called subcoordinate representation. The main feature of the subcoordinaterepresentation of a p-adic function is that the values of the function f are given in the canonical form of the representation of p-adic numbers. The function f itself is determined by a tuple of p-valued functions from the set {0, 1,..., p-1} into itself and by the order in which these functions are used to determine the values of f. We also give formulae that enable one to pass from the subcoordinate representation of a 1-Lipschitz function to its van der Put series representation. The effective use of the subcoordinate representation of p-adic functions is illustrated by a study of the feasibility of generalizing Hensel's lemma.