A theoretical examination is made of the impedance of a biconical antenna, based upon a method devised by Schwinger in studying the discontinuity problems of a wave guide. In the present analysis, an integral equation to determine the aperture field is obtained by matching the tangential electric and magnetic fields along the boundary sphere. Using this integral equation, the effective terminating admittance of the antenna can be expressed in a form that is stationary with respect to small variations in the aperture field. It is shown that the zeroth‐order solution of the admittance function thus obtained is the same as the one that Smith derived by neglecting all the high order waves in the interior region except the principal mode. For small‐angle cones, the present formulation yields the same exact solution obtained previously, based upon several different methods. The paper also contains a discussion of the first‐order approximate solution which is applicable to both small‐ and wide‐angle cones. The analysis includes a detailed treatment of a method by which the characteristic values and characteristic functions for a given cone may be found approximately, but very accurately; as well as certain integrals involving the product of Legendre functions.