Halle´n's complex integral equation for the current in a cylindrical antenna is separated into two real integral equations for the components of current in phase and in phase‐quadrature with the driving voltage. Each of these equations is solved by iteration using zeroth‐order currents and vector‐potential differences to define expansion parameters. It is shown that for electrical half‐lengths near odd multiples of a quarter‐wavelength at least a third‐order solution is required in order to determine accurately the component of current in phase with the driving voltage and the conductance. Conductances for a range of radii are evaluated by the new third‐order formula and compared with the King‐Middleton second‐order values and with the experimental data of Hartig. The new formula agrees excellently with experimental results ath=&lgr;0/4, whereas the earlier second‐order formula has by far its greatest percent error—near 8 to 10 percent—in a small range near resonance. It is concluded that for antennas near resonance, just as for very short and very long antennas, adequate account must be taken in the iteration of both components of current.