The paper deals with a method for global minimization of increasing positively homogeneous functions over the unit simplex, which is a version of the cutting angle method. A new approach for solving the auxiliary problem in the cutting angle method is proposed. In the method, the auxiliary problem is reformulated as a certain combinatorial problem. The modified version of the cutting angle method is also applied for Lipschitz functions that could be expressed as increasing positively homogeneous functions. We report results of numerical experiments which demonstrate that the proposed algorithm is very efficient in the search for a global minimum.