Several bearingless flux-switching motors have been implemented recently. These magnetically levitated drives create radial suspension forces and drive torque. They represent permanent-magnetic excited synchronous machines but feature rotors without any permanent-magnetic but salient rotor poles. A heteropolar air-gap field is excited by stator permanent magnets, which are located in-between the stator teeth. The rotor teeth change the permanent-magnetic flux paths and switch the magnetic flux linked with the stator coils, which are concentrically wound around the stator teeth. Typical bearingless flux-switching motors feature twelve stator teeth and ten salient rotor poles. However, all the presented designs up to now feature interior rotors. In this work an exterior rotor composition is considered for the first time in bearingless flux-switching motors. Design rules for a proper selection of the rotor tooth number are given using an analytic motor model considering suspension force and drive torque generation. To verify the theoretical results a prototype flux-switching motor with exterior rotor is optimized and manufactured. Its characteristic data is measured and compared to the referring 3D finite-element simulation results.