With the aid of methods previously developed, an approximate expression is obtained for the difference from unity of the transmission coefficient for plane waves at normal incidence of a large aperture of rather general form in a plane perfectly-conducting screen. The coefficient is expressed in the form of one or more line integrals taken around all (or part) of the aperture rim. These may be evaluated analytically in certain cases, e.g. a circular or elliptical aperture. In the former case the result agrees with that derived elsewhere; the ellipse is considered in some detail in the present paper, and the transmission coefficient is evaluated for a range of eccentricities. The results appear to be in qualitative agreement with the limited experimental data available.