By following the basic principles of the design of nonfullaperture Luneburg lenses, a new solution, or a new family of lenses has been found. The new lens has in the outer shell the profile of a refractive index characterized as n=exp(P2/h2). In practice, each particular solution is characterized by the focal length and the value of the refractive index at the edge of the lens. The value of the refractive index at the edge can be arbitrarily selected within a certain range. This range is different for different focal lengths.