A clean and well-ordered (001) surface of a slightly nonstoichiometric natural single crystal of magnetite has been prepared under ultrahigh vacuum conditions by in situ thermal annealing. The surface was carefully characterized by low energy electron diffraction, Auger electron spectroscopy, and x-ray photoelectron spectroscopy prior to our scanning tunneling microscope investigations. Atomic resolution was achieved by using either tungsten or in situ prepared ferromagnetic iron tips. In contrast to the results obtained with the tungsten tips, the ferromagnetic probe tips revealed an atomic-scale contrast between the different magnetic iron ions of magnetite on the octahedrally coordinated B sites which form static arrays of pairs with short-range order. The clean magnetite (001) surface appears to be in a Wigner glass state even at room temperature with electron pairs localized on adjacent ions as the basic unit. The degree of order is likely to be limited by the slight nonstoichiometry of the magnetite sample as deduced from temperature-dependent measurements of the electrical resistivity.