The regions of precipitation of high-energy electrons injected into the near-Earth space by a point source have been determined on the basis of numerical calculations of relativistic electron trajectories in the geomagnetic field approximated by the magnetic dipole field. It has been found that the precipitation regions have pronounced structure in the form of alternating areas composed of points, attainable for electrons from the injector, and "shadow" zones closed for electrons emitted by the injector. This structure is observed in most cases of practical importance when injectors are located in geostationary or low-altitude orbits and the electron energy is about tens of GeV. The precipitation regions are localized in the magnetic latitude band ψ < 40° for the near-Earth positions of the injector at any electron energies. In this case, the high-latitude region and a significant part of the midlatitude region appear to be, in principle, unattainable for electrons injected in the immediate vicinity of the Earth.