The class $P_n(I)$ of matrix monotone functions of order $n$, defined on an open interval $I$, is considered in this paper. Explicit examples are given to prove that if $I$ is different from the whole real line, then $P_{n+1}(I)$ is a proper subset of $P_n(I)$ for each natural number $n$. The subhomogeneous C*-algebras are then characterized in terms of matrix monotone functions.