The valid region for the application of the conventional Improved Circuit Theory (ICT) in the analysis of wire antennas is established. To further extend the application of ICT to the analysis of much longer antennas, Tai's trial function is used to derive new formulas for the impedance matrix. Unlike the conventional ICT trial function, Tai's trial functions lead to input impedances which are finite irrespective of antenna length. Results of the new ICT impedance formulas are comparable in accuracy with the general method of moments. Moreover, since all the elements of the new formula have been expressed in closed-form, the resulting ICT algorithm is still superior in terms of computer running time with lesser storage requirement compared to other conventional methods like method of moments. This would enhance ICT applications in CAD/CAE systems.