In this paper some properties of the multivariate Beta distributions are discussed. Specifically it is shown that the density of the multivariate Beta I distribution can be decomposed as a product of independent ordinary Beta I densities and the Dirichlet densities, while the density of the multivariate Beta II distribution as a product of independent ordinary Beta II densities and the inverted Dirichlet densities. Some extentions of the results to the generalized multivariate Beta distributions are indicated.