The binary-encounter-Bethe (BEB) model of Kim and Rudd for total ionization cross-sections by electron impact is re-examined when the target is an atom with principal quantum number n greater than or equal to 3, or a molecule consisting of one or mon atoms with n greater than or equal to 3. It is shown that the use of relativistic effective core potential (RECP) for heavy atoms removes the need for the empirical scaling used previously. BEB cross-sections of Ar, Kr, Xe, Cl, Pr, I, and WF6 calculated using RECP are found to be in good agreement with available experimental data, especially in the low-energy region.