A simple model is proposed for nematogenic molecules that favor perpendicular orientations as well as parallel ones. (Charged rods, for example, show this antagonistic tendency.) When a small disorienting field is applied along z, a low-density phase N- of nematic order parameter S-z<0 coexists with a dense biaxial nematic N-b. (At zero field, N- becomes isotropic and N-b uniaxial.) But at stronger fields, a new phase N+4, invariant under π/2 rotations around the field axis, appears in between N- and N-b. Prospects for finding the N+4 phase experimentally are briefly discussed.