In this article, we construct a submodular function using the rank function of a matroid and study induced matroid with constructed polymatroid, then we relate some properties of connectivity of new matroid with the main matroid.

For a set  of circuits of a matroid M, G(B(M), ) is defined by the graph with one vertex for each basis of M, in which two basis B 1 and B 2 are adjacent if B 1 ∪ B 2 contains exactly one circuit and this circuit lies in . For two elements of a and b of ground set of a binary matroid M a splitting matroid M a,b is constructed. It is specified by two collections of circuits  0 and  1 dependent with collections of circuits of M. We want to study connectivity of G(B(M a,b),  0) and G(B(M a,b),  1).