  In this article, we prove that a quotient of a K3 surface by a free Z_2+Z_2
action does not admit any metric of positive scalar curvature. This shows that
the scalar flat anti self-dual metrics (SF-ASD) on this manifold can not be
obtained from a family of metrics for which the scalar curvature changes sign,
contrary to the previously known constructions of this kind of metrics on
manifolds of b+=0.
