In this paper, we present a new approach for com-puting Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. The pro-posed method constructs a continuous piecewise affine (CPA) function on a compact subset of the state space containing the origin, given a suitable triangulation or partition of the compact set and values at the vertices of the triangulation. Here, the vertex values are fixed using a function from a classical con-verse Lyapunov theorem originally due to Yoshizawa. Several numerical examples are presented to illustrate the proposed approach.