  Suppose $w$ is a sense-preserving harmonic mapping of the unit disk
$\mathbb{D}$ such that $w(\mathbb{D})\subseteq\mathbb{D}$ and $w$ has a zero of
order $p\geq1$ at $z=0$. In this paper, we first improve the Schwarz lemma for
$w$, and then, we establish its boundary Schwarz lemma. Moreover, by using the
automorphism of $\mathbb{D}$, we further generalize this result.
