This work deals with a new methodology for the implementation of high-resolution (HR) schemes employed to advect the volume fraction in the volume of fluid (VOF) method, in which the numerical stability and convergence depend heavily on the numerical advection scheme and implementation method. The proposed method is based on the normalized weighting factor (NWF) method, which linearizes the normalized interpolation profile and rewrites the face value directly using the donor, acceptor, and upwind nodes. However, unlike the NWF, which is fully implicit and results in pentadiagonal linear systems, the new modified normalized weighting factor (MNWF) method only forms the implicit terms with the contribution of the donor and acceptor nodes, while the contribution of the upwind node explicitly forms part of the source term. Therefore, the method results in a tridiagonal linear system. The comparison of the new method with the deferred correction (DC), downwind weighting factor (DWF), and the RNWF methods shows that the MNWF requires about 5%-25% fewer iterations than DC and RNWF, and around 10%-85% less than DWF. Thus, a similar order of accuracy of the results can be obtained with less computational time.