This paper introduces an alternative proof for Weber's axiomatization of the random order values. In this proof, we make use of a combinatorial result that has recently been discussed by Vasil'ev [Vasil'ev, V.A., 2003. Extreme points of the Weber polyhedron. Discretnyi Analiz i Issledovaniye Operatsyi Ser.1, v.10, no. 2:17-55.]. In addition, we provide a new and intuitive proof for this combinatorial result.