The feedpoint singularity in the current on an axially symmetric antenna with a slice generator is removed by a well-defined subtraction procedure involving a new integral equation for the antenna current. In contrast to the usual linear antenna theory in which an open-ended tube is chosen as the basic model for the antenna, this paper considers a model in which the antenna is either a sliced closed hollow shell or a sliced solid conductor. The nonsingular portion of the current is shown to have several desirable features. One of the major desirable features is that it yields an input admittance of an infinite cylindrical antenna comparable to that obtained by Duncan's extrapolation procedure. Another is that the reciprocity relation between the transmitting and receiving properties of an antenna can be formulated rigorously in terms of the finite parts of the currents.