The leading idea to the algorithm presented in this work could be used to solve hard nonlinear problems ; these that can hardly be solved by classical schemes. This idea is herein explained for the solution of a class of stiff normal contact problems between two solids. For these, it consists in a scheme that constructs, iteratively, approximate contact models, leading to softer, still nonlinear, problems, better suited to classical schemes, whose convergent solution solves the stiff contact problem. Numerical results show the remarkable performance of this algorithm, labeled extended-Newton scheme.