A new derivative-free optimization method for unconstrained optimization of partially separable functions is presented. Using average curvature information computed from sampled function values the method generates an average Hessian-like matrix and uses its eigenvectors as new search directions. Numerical experiments demonstrate that this new derivative free optimization method has the very desirable property of avoiding saddle points. This is illustrated on two test functions and compared to other well known derivative free methods. Further, we compare the efficiency of the new method with two classical derivative methods using a class of testproblems. publishedVersion