<正> The class of distributions on Rm, 1≤m<∞ which are the m-dimensionalmarginal distributions of orthogonally invariant distribution on Rm+n wascharacterized by Eaton (1981). In this paper, the class of distributions onRm×p, 1≤m<∞ which are the m×p marginal distributions of othogonallyinvariant distribution on Rm+n×p is characterized.