It is shown that a density of states (DOS) proportional to the excitation energy, a so-called polar-like DOS, can arise in odd-parity states, with the superconducting gap vanishing at points even though the spin-orbit interaction for Cooper pairing is strong. Such gap structures are realized in the nonunitary states, F 1u (1, i, 0), F 1u (1, ε, ε 2 ), and F 2u (1, i, 0), classified by Volovik and Gorkov (1985 Sov. Phys.-JETP 61 843). This is due to the gap vanishing in a quadratic manner around a point on the Fermi surface.