Let $k$ and $n$ be fixed, $k\ge 1$, $n\ge 1$, and let $S$ be a simply connected orthogonal polygon in the plane. For $T\subseteq S,T$ lies in a staircase $n$-convex orthogonal polygon $P$ in $S$ if and only if every two points of $T$ see each other via staircase $n$-paths in $S$. This leads to a characterization for those sets $S$ expressible as a union of $k$ staircase $n$-convex polygons $P_i$, $1\le i\le k$.