On Serial Symmetric Exchanges of Matroid Bases

We study some properties of a serial (i.e., one‐by‐one) symmetric exchange of elements of two disjoint bases of a matroid. We show that any two elements of one base have a serial symmetric exchange with some two elements of the other base. As a result, we obtain that any two disjoint bases in a matroid of rank 4 have a full serial symmetric exchange