In this note, we prove the following results: (1) if $\dim (N) \geqslant 3$ then $\mathrm{Ass}(H_I^i(M, N))$ is finite for all $i\geqslant 0$; (2) Let $d = \dim(R)$ and $s(I, M) = \mathrm{depth}(M/I^nM)$ for some large $n$. If $N$ has finite injective dimension then we have $H_I^i(M, N) = 0$ for all $i > d − s(I, M),$ $H_I^d(M, N)$ is Artinian, and $\mathrm{Supp}(H_I^{d−1}(M, N))$ is finite.