  The generalized Kneser hypergraph $KG^{r}(n,k,s)$ is the hypergraph whose
vertices are all the $k$-subsets of $\{1,\ldots ,n\}$, and edges are $r$-tuples
of distinct vertices such that any pair of them has at most $s$ elements in
their intersection. In this note, we show that for each non-negative integers
$k, n, r, s$ satisfying $n \geq r(k-1)+1$, $k > s\geq 0$, and $r\geq 2$, we
have $$\chi
({KG}^{r}(n,k,s))\geq\left\lceil\frac{n-r(k-s-1)}{r-1}\right\rceil,$$ which
improves the previously known result by Alon--Frankl--Lov\'{a}sz.
