  We show that the co-rays to a ray in a complete non-compact Finsler manifold
contain geodesic segments to upper level sets of Busemann functions. Moreover,
we characterise the co-point set to a ray as the cut locus of such level sets.
The structure theorem of the co-point set on a surface, namely that is a local
tree, and other properties follow immediately from the known results about the
cut locus. We point out that some of our findings, in special the relation of
co-point set to the upper lever sets, are new even for Riemannian manifolds.
