Mapping of the radiation belt environment in the classical (B, L) invariant coordinates is rather poorly resolved at low altitudes where the SAMPEX and DEMETER missions are collecting scientific data. This lack of adequate spatial resolution at low altitudes has been pointed out since 1986. A simple solution to this standing problem is proposed in this article. We recall alternative coordinates that were proposed in the 90s to improve the spatial resolution of binning meshes and radiation belt maps in the lowaltitude region, i.e., near the atmospheric cutoff. Next, we define a new coordinate: The "invariant altitude," hinv, that we recommend instead of B or other invariant drift shell coordinates like B/B0 or α0, the equatorial pitch angle. In McIlwain's reference dipole, the new coordinate, hinv, corresponds to the altitude (in units of km) of mirror points of particles which have given values of B and I or L, calculated by using a geomagnetic field model like the International Geomagnetic Reference Field. The advantages and limitations of the new hinv coordinate are presented. For illustration, the distributions of the omnidirectional fluxes of electrons and protons predicted by the standard AE8 and AP8 radiation belt models are displayed using this new invariant coordinate, as well as by using alternative invariant coordinates like B/B0 or α0. A set of orbits of the SAMPEX, DEMETER, and CRRES spacecraft are displayed in these different coordinate systems to illustrate the advantage of using the invariant altitude hinv to map the radiation belt environment at low altitudes.