Low-temperature magnetization of hematite within the basal plane has been studied in a collection of natural crystals by means of torque magnetometry. Comparison between the torque curves at room temperature and at 77 K allows identification of a weak ferromagnetic moment constrained within the basal plane at temperatures well below the Morin transition. Annealing the samples produces the expected reduction of the weak ferromagnetic moment, but there is also a relationship between the ferromagnetic moment before and after annealing. Low-temperature measurements after the annealing experiment reveal the presence of a weak ferromagnetic moment that survives the annealing. This observation suggests the magnetic structure of natural hematite crystals below the Morin transition can still be a carrier of magnetization.