Abstract: Last time we defined what it means to be a Minkowski weight over a k-skeleton of a fan (complete or not). To a loopless matroid, there is an associated simplicial fan called Bergman fan. Following de Medrano, Rincon and Shaw we will define the CSM classes of a loopless matroid as Minkowski weights over this fan. We will show that it satisfies the balancing condition. This will involve some combinatorial machinery concerning matroid that we will review.