  We study homogenous Weyl connections with non-positive sectional curvatures.
The Cartesian product $\mathbb S^1 \times M$ carries canonical families of Weyl
connections with such a property, for any Riemmanian manifold $M$. We prove
that if a homogenous Weyl connection on a manifold, modeled on a unimodular Lie
group, is non-positive in a stronger sense (streched non-positive), then it
must be locally of the product type.
