An orbitalis muscle is a rudimentary nonstriated muscle (smooth muscle) that crosses from the infraorbital groove and sphenomaxillary fissure and intimately united with the periosteum of the orbit. It is often called Muller's muscle. One characteristic of Horner's Syndrome is enophthalmos (retraction of the eyeball into the orbit due to paralysis of the orbitalis muscle that spans the inferior orbital fissure). Its function is eyeball protrusion. [ http://en.wikipedia.org/wiki/Orbitalis_muscle ]