  Let $S_k(n)$ be the maximum number of orientations of an $n$-vertex graph $G$
in which no copy of $K_k$ is strongly connected. For all integers $n$, $k\geq
4$ where $n\geq 5$ or $k\geq 5$, we prove that $S_k(n) = 2^{t_{k-1}(n)}$, where
$t_{k-1}(n)$ is the number of edges of the $n$-vertex $(k-1)$-partite Tur\'an
graph $T_{k-1}(n)$, and that $T_{k-1}(n)$ is the only $n$-vertex graph with
this number of orientations. Furthermore, $S_4(4) = 40$ and this maximality is
achieved only by $K_4$.
