In magnetically ordered crystals, which are deprived of anti‐inversion as a symmetry operation, a new magnetooptical effect is permitted. It consists in appearance of a birefringence of the linear polarized light directly proportional to the magnetic field strength as opposed to the quadratic Cotton‐Mouton and Voight effects. The appearing birefringence is connected with inducing the nonequivalency of magnetic sublattices by a magnetic field. The sign of the linear magnetooptical effect depends on the directions of the sublattice magnetic moments and the magnetic field strength. It is determined by sign of the antiferromagnetic vector projection on some axis only if the magnetic field direction is constant. This circumstance gives a possiblity of visualizing the regions of the crystals having oppositely oriented antiferromagnetic vectors. The visual observation of the 180‐degree antiferromagnetic domains in the two‐sublattice antiferromagnetic cobalt fluorite by means the new linear magnetooptical effect is reported.