A new method for a narrowing of sphere of a search of an optimum decision in a clustering problem is proposed. A constant parameters for any problem are revealed, and a conformity with natural laws of changing objective function values depending on them are established. One of them is a finite sequence (a variant of partitioning) which is generated a combination of elements of combinatorial matrix. The rules of formation this sequence are defined. A conformity with natural laws of changing objective function values depending on these variants of partitioing is analised. It is proved that variants of partitioning in a clustering problem consists of subsets. It is shown, that the variants of partitioning for which the objective function take eithher maximum or minimum, can be contained in different subsets or into one of them.