  A central arrangement $\A$ of hyperplanes in an $\ell$-dimensional vector
space $V$ is said to be {\it totally free} if a multiarrangement $(\A, m)$ is
free for any multiplicity $ m : \A\to \Z_{> 0}$. It has been known that $\A$ is
totally free whenever $\ell \le 2$. In this article, we will prove that there
does not exist any totally free arrangement other than the obvious ones, that
is, a product of one-dimensional arrangements and two-dimensional ones.
