  Let $(R,\fm)$ be commutative Noetherian local ring. It is shown that $R$ is
Cohen--Macaulay ring if there exists a Cohen--Macaulay finite (i.e. finitely
generated) $R$--module with finite upper Gorenstein dimension. In addition, we
show that, in the Intersection Theorem, projective dimension can be replaced by
quasi--projective dimension.
