A nonlinear function has been introduced for indexing the disagreement degree of a group of judgment matrices (Weiwu Fang, 1994). It has many good properties and may be applied in decision making and information processes. In this paper, we will discuss a global optimization problem concerned with the global maximum of this function which is constrained on some sets of matrices. Because the size of matrix groups in the problem is arbitrary and the number of local maximum solutions increases exponentially, numerical methods are not suitable and formalized results are desired for the problem. By an approach somewhat similar to the branch and bound method, we have obtained some formulae on global maximums, a sufficient and necessary condition of the function taking the maximums, and some maximum solution sets.