Let $(R,\fm)$ be a commutative Noetherian local ring, $\fa$ an ideal of $R$ and $A$ an Artinian $R$-module. Let $t$ be a positive integer such that the local homology module $H_i^{\fa}(A)$ is Artinian for all $it$. In particular, the set $\V({\fa})\cap\Coass(H_{\fa}^t(M))$ is finite.
