  We prove two inequalities for the direct and truncated correlation for the
nearest-neighboor one-dimensional Edwards-Anderson model with symmetric
quenched disorder. The second inequality has the opposite sign of the GKS
inequality of type II. In the non symmetric case with positive average we show
that while the direct correlation keeps its sign the truncated one changes sign
when crossing a suitable line in the parameter space. That line separates the
regions satisfying the GKS second inequality and the one proved here.
