A generalization of the theorem on forming a matroid from parts

A generalization of the theorem on forming a matroid from parts is proved, i.e., given a finite set subdivided into some blocks, each of which is supplied with a matroid structure, and assuming that the ranks of every union of certain blocks are prescribed in such a way that the conditions on the rank function of a matroid are fulfilled, one can extend the rank function to all the subsets of the original set in such a way that the latter becomes a matroid.