  Let $\A$ be a line arrangement in the complex projective plane $\PP^2$.
Denote by $M$ its complement and by $\M$ the set of points in $\A$ with
multiplicity at least 3. A rank one local system $\mathcal{L}$ on $M$ is
admissible if roughly speaking the dimension of the cohomology groups
$H^m(M,\mathcal{L})$ can be computed directly from the cohomology algebra
$H^{*}(M,\Bbb{C})$. In this work, we give a sufficient condition for the
admissibility of all rank one local systems on $M$.
