Topological graphs and their C*-algebras were introduced by Katsura and extend the concept of directed graphs to locally compact topologies on the edge and the vertex spaces. Proper factor maps are defined between topological graphs which contravariantly induce a *-homomorphism between the corresponding C*-algebras. We generalise this notion to include non-proper continuous maps which induce nondegenerate *-homomorphisms between the corresponding C*-algebras. This allows us to have new kinds of morphisms in the theory of graph algebras and gives rise to some natural examples.