An earlier theoretical treatment of the Cˇerenkov radiation excited by the passage of a bunched electron beam moving parallel to a dielectric medium at a small distance is extended to the case of a medium with a complex index of refraction. It is found that under suitable conditions, the use of a ferrite material as a medium can in principle enhance the radiated power. This effect is analyzed in terms of the work done by the beam on the field and the coupling between the beam and the medium.