  Let $\mathfrak{a}$ be an ideal of a commutative Noetherian ring $R$ and $M$ a
finitely generated $R$-module. In this paper we proved that if
$\operatorname{Supp}\mathfrak{F}_\mathfrak{a}^i(M)$ is finite for all $i<t$,
then so is $\operatorname{Ass}(\mathfrak{F}_{\mathfrak{a}}^t(M))$.
