Let R be a commutative Noetherian ring, a system of ideals of R, and M a finitely generated R-module. Suppose that a 2 and t is a non-negative integer. It is shown that if Exti R(R/a,Hj (M)) is finitely generated for all i and all j < t, then Exti R(R/a,Ht(M)) is finitely generated for i = 0, 1. In particular, if R is a local ring of dimension at most 2, then Exti R(R/a,Hj (M)) is finitely generated for all i, j.
