Given a set S of data points in R2 and corresponding data val ues for a specific non-convex surface, the unit hyperbolic paraboloid, we consider the problem of finding a locally optimal triangulation of S for the linear approximation of this surface. The chosen optimality criterion will be the L2 norm: it means that we will try to find directly a triangulation that minimizes the L2 error made when approximating locally the surface with triangles.