The angle distribution for fission fragments is considered at high excitation levels; in this case the angular momentum is distributed over a large number of nucleons and statistical theory can be applied to the nucleus. The distribution of states of the “transition” nucleus over values of the quantity K. the projection of the moment of the compound nucleus along the fission axis, is computed. The most probable state is found to be that with K = 0, which, in the case of neutron-induced fission leads to the appearance of maxima in the fragment angle distribution at 0 ° and 180 °. The results are compared with experiment; the moment of inertia of the “transition” nucleus with respect to the symmetry axis is determined (fission direction). The fragment angle distribution for fission induced by charged particles and γ-rays is also analyzed.