Several CAD applications require a surface model of the modeled object consisting of a mesh of triangular facets. In this paper, a new algorithm for triangulation of trimmed surfaces is presented. The algorithm generates a triangulation that approximates the initial surface within a predefined tolerance. The approximation is conformal, without cracks in edges: a closed polyhedron is obtained in the case of a closed initial surface. The proposed algorithm improves the algorithm presented in (Brunet and Vigo, 1995) because it is based on more precise bounds which take into account the directional behavior of local surface curvature, and the resulting triangulation has a lower number of triangles.