  A ring $R$ is strongly clean provided that every element in $R$ is the sum of
an idempotent and a unit that commutate. Let $T_n(R,\sigma)$ be the skew
triangular matrix ring over a local ring $R$ where $\sigma$ is an endomorphism
of $R$. We show that $T_2(R,\sigma)$ is strongly clean if and only if for any
$a\in 1+J(R), b\in J(R)$, $l_a-r_{\sigma(b)}: R\to R$ is surjective. Further,
$T_3(R,\sigma)$ is strongly clean if $l_{a}-r_{\sigma(b)},
l_{a}-r_{\sigma^2(b)}$ and $l_{b}-r_{\sigma(a)}$ are surjective for any $a\in
U(R),b\in J(R)$. The necessary condition for $T_3(R,\sigma)$ to be strongly
clean is also obtained.
