We apply the continuum-distorted-wave approximation within the framework of the independent-event model to calculate the ratio ({ital R}) of double-to-single ionization cross sections of He by N{sup 7+} projectiles. Following Deb and Crothers (J. Phys. B 23, L7999 (1990)), we calculate the double-ionization probability as {ital P}{sub 1}{ital P2}, whereas the single-ionization probability is taken to be 2{ital P}{sub 1}(1{minus}{ital P}{sub 1}). Here, {ital P}{sub {ital i}} ({ital i}=1,2) is the probability of ionizing the {ital i}th electron from He. The values of {ital R} found in the 10--40-MeV/u impact-energy range are similar to those obtained in the somewhat different forced-impulse theory of Reading and Ford (Phys. Rev. Lett. 58, 543 (1987)) and by the semiempirical fit of Knudsen {ital et} {ital al}. (J. Phys. B 17, 3545 (1984)), but are much smaller in absolute value than the corresponding measurements of Heber {ital et} {ital al}. (Phys. Rev. Lett. 64, 851 (1990); Nucl. Instrum. Methods B 56/57, 15 (1991)).