  Fault tolerance of an $(n,k)$-star network is measured by its $h$-super
connectivity $\kappa_s^{(h)}$ or $h$-super edge-connectivity $\lambda_s^{(h)}$.
Li {\it et al.} [Appl. Math. Comput. 248 (2014), 525-530; Math. Sci. Lett. 1
(2012), 133-138] determined $\kappa_s^{(h)}$ and $\lambda_s^{(h)}$ for $0\leq
h\leq n-k$. This paper determines
$\kappa_s^{(h)}=\lambda_s^{(h)}=\frac{(h+1)!(n-h-1)}{(n-k)!}$ for $n-k\leq h
\leq n-2$.
