  We study cohomology with coefficients in a rank one local system on the
complement of an arrangement of hyperplanes $\A$. The cohomology plays an
important role for the theory of generalized hypergeometric functions. We
combine several known results to construct explicit bases of logarithmic forms
for the only non-vanishing cohomology group, under some nonresonance conditions
on the local system, for any arrangement $\A$. The bases are determined by a
linear ordering of the hyperplanes, and are indexed by certain
``no-broken-circuits" bases of $\A$. The basic forms depend on the local
system, but any two bases constructed in this way are related by a matrix of
integer constants which depend only on the linear orders and not on the local
system. In certain special cases we show the existence of bases of monomial
logarithmic forms.
