Let R be a commutative Noetherian ring, a an ideal of R, and M a non-zero nitely generated R-module. Let t be a non-negative integer. It is shown that dim SuppHi a (M) 1 for all i < t if and only if there exists an ideal b of R such that dimR=b 1 and Hi a (M) = Hi b(M) for all i < t. Moreover, we prove that dim SuppHi a(M) dimM i for all i.
