  Let $X$ be a ball quasi-Banach function space on $\mathbb R^{n}$ and
$h_{X}(\mathbb R^{n})$ the local Hardy space associated with $X$. In this
paper, under some reasonable assumptions on $X$, the infinite and finite atomic
decompositions for the local Hardy space $h_{X}(\mathbb R^{n})$ are established
directly, without relying on the relation between $H_{X}(\mathbb R^{n})$ and
$h_{X}(\mathbb R^{n})$. Moreover, we apply the finite atomic decomposition to
obtain the dual space of the local Hardy space $h_{X}(\mathbb R^{n})$.
Especially, the above results can be applied to several specific ball
quasi-Banach function spaces, demonstrating their wide range of applications.
