In this paper we define a discrete quasi -Newton algorithm which uses only function values for finding an optimal solution to the problem $min \{ \phi(x) \| x \in X \}$, where X is a convex polytope. It is shown that using this algorithm one can reduce the initial problem to a finite number of subproblems of the type $min \{ \phi(x) \| x \in C \}$, where C is a linear manifold . It is also shown that each cluster point of the sequence gene rated by the algorithm is an optimal point of the considered optimization problem.