  Let $1<p\le4$ when $n=1$ and $1<p< 3+\frac{1}{n-1} $ when $n\ge2$. We obtain
the second-order horizontal Sobolev $HW^{2,2}_{\rm loc} $-regularity of
$p$-harmonic functions in the Heisenberg group $\mathbb H^n$. This improves the
known range of $p$ obtained by Domokos and Manfredi in 2005.
