In this paper we introduce a new way of representation of p-adic functions, namely, the sub-coordinate representation. The main feature of such representation is that the values of a function f are given in the canonical form of representation of p-adic number. In the sub-coordinate representation thefunction f is determined by a set of p-valued functions that map a set {0,1,...,p - 1} into itself, and by the order of these functions. As one of the applications ofthe sub-coordinate representation, we study a problem of generalization of Hensel's lifting lemma.