When magnetic skyrmions are moved via currents, they do not strictly travel along the path of the current, instead their motion also gains a transverse component. This so-called skyrmion Hall effect can be detrimental in potential skyrmion devices because it drives skyrmions towards the edge of their hosting material where they face potential annihilation. Here we experimentally modify a skyrmion model system—an atomic Pd/Fe bilayer on Ir(111)—by decorating the film edge with ferromagnetic Co/Fe patches. Employing spin-polarized scanning tunneling microscopy, we demonstrate that this ferromagnetic rim prevents skyrmion annihilation at the film edge and stabilizes skyrmions and target states in zero field. Furthermore, in an external magnetic field the Co/Fe rim can give rise to skyrmions pinned to the film edge. Spin dynamics simulations reveal how a combination of different attractive and repulsive skyrmion-edge interactions can induce such an edge-pinning effect for skyrmions.