Let $\cal M$ be a finite piecewise linear (pl) manifold of $IR^n$, and $P$ : $IR^n \rightarrow IR^n$ be pl with respect to $\cal M$, i.e. $P$ is affine on each set in $\cal M$. The branching number of $\cal M$, Kuhn and Lowen [8], is the maximum number of sets in $\cal M$ that can contain any common face of codimension 2. [8, Thm. 5.3] shows that if $\cal M$ has branching number less than or equal to 4, then $P$ is a homeomorphism if and only if it is coherently oriented, i.e. the determinants of $P$ on the sets in $\cal M$ have the same nonzero sign. Let $C$ be a nonempty polyhedral convex set in $IR^n$, and $A \in IR^{nxn}$. Robinson [14] defines a finite pl manifold $\cal N_C$ of $IR^n$ called the normal manifold of $C$; and the normal map $A_C$ : $IR^n \rightarrow IR^n$ induced by ($A, C$), which is pl with respect to $\cal N_C$. [14, Thm. 4.3] shows that $A_C$ is homeomorphic if and only if it is coherently oriented. We show that $\cal N_C$ has branching number less than or equal to 4, hence Robinson's result is actually a corollary of Kuhn and Lowen's. Key Words: Piecewise linear, piecewise affine, branching number, normal map, pl-normal, normal manifold, homeomorphism, coherently oriented.