1 IntroductionThe bases of a matroid have many good properties. Combinatorial optimization problemsamong them can be effectively solved. In this paper, we consider the conjecture about thebases of a matroid proposed by White . While this conjecture has occasionally beenstated in terms of algebraic expressions, it is closely related to combinatorial problems.Our proof adopts a combinatorial approach.A matroid has several equivalent definitions. We define a matroid by a set of subsetsthat satisfies the exchange axiom. A family B of sets is the collection of bases of a matroidif it satisfies the exchange axiom given below....