  Let $\mathcal{R}$ be a $2$-torsion free commutative ring with unity, $X$ a
locally finite pre-ordered set and $I(X,\mathcal{R})$ the incidence algebra of
$X$ over $\mathcal{R}$. If $X$ consists of a finite number of connected
components, in this paper we give a sufficient and necessary condition for each
commuting map on $I(X,\mathcal{R})$ being proper.
