Coupling with the Modified-Grid Unconstrained Optimization Algorithm we introduced in our previous paper (Cheung and Ng, 1995), we have been able to developed a new Algorithm for Nonlinear Optimization capable of working with nonsmooth problems. This Algorithm is based on the Principle of Support by smooth Hypersurfaces. This old but very sound concept has been revitalized by the introduction of a specially constructed Generalized Lagrangian Function and a new penalty updating formula. We have proved without differentiable assumptions that the solution always exists under some mild condition and that the algorithm converges. The Algorithm has performed very well on test runs and on comparison with some popular packages. It offers an easy extension to a global optimization algorithm.