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We have shown that finite-difference time-domain (FDTD) electromagnetic computations for a conductor system having a radius smaller than 0.15Deltar or larger than 0.65 Deltar (Deltar is the lateral side length of cells employed), modeled using arbitrary-radius-wire representations proposed so far with a time increment determined from the upper limit of Courant's stability condition, result in numerical instability. A primary factor causing this numerical instability is that the speed of waves propagating in the radial direction from the wire in the immediate vicinity of the wire exceeds the speed of light, and therefore, Courant's condition is not satisfied there. It is further shown that for these cases, the arbitrary-radius-wire representation can be improved by modifying the material parameters for the axial field components closest to the wire as well as those for the radial electric and circulating magnetic field components. The improved wire representation is effective in representing a wire whose radius ranges from 0.0001Deltar to 0.9Deltar.