  We introduce a dual logarithmic residue map for hypersurface singularities
and use it to answer a question of Kyoji Saito. Our result extends a theorem of
L\^e and Saito by an algebraic characterization of hypersurfaces that are
normal crossing in codimension one. For free divisors, we relate the latter
condition to other natural conditions involving the Jacobian ideal and the
normalization. This leads to an algebraic characterization of normal crossing
divisors. As a side result, describe all free divisors with Gorenstein singular
locus.
