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Magnetic properties of magnetite (Fe3O4) powders, milled for various times up to 15 h, are studied by magnetization measurements. For the starting powder, like in the bulk single crystal, the approach to magnetic saturation is mainly ruled by the usual 1/H and 1/H2 terms. But for the milled samples, as the grain size decreases, a 1/H1/2 term rises as the leading term and is interpreted in the framework of the theory of Chudnovsky et al. accounting for the effect of a random anisotropy generated near the surface, aside from a large constant high field susceptibility related to the canted spins at the surface.