With a very elaborate method, the authors verify the accuracy of the screemng potential (SP) computed by the consideration of the short range order effect for the classical One-Component-Plasmas (OCP). The authors obtain a compact, effective form for the SP, useful for the computerization and find the exact value of Jancovici coefficient. The agreement between our formula and the Monte Carlo simulation data proves completely satisfactory. As a result, the calculation for this quantity can be extended by an extrapolation to the region where the crystallization of the OCP system is thought to appear and the expression for the SP at this phase change point will be presented.