Let M be a matroid defined on a finite set E and L ⊂ E . L is locked in M if $\"\"$ and $\"\"$ are 2-connected, and $\"\"$ . In this paper, we prove that the nontrivial facets of the bases polytope of M are described by the locked subsets. We %K Bases Polytope %K Facets %K Locked Subsets %K Maximum-Weight Basis Problem %K Polynomially Locked Matroids %K Matroid Oracle %K Testing Unformity of a Matroid %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=81695