A kind of modified hourglass worm drives, which is frequently called the type II worm gearing for short, has various favorable meshing features. Nevertheless, its sole shortcoming is the undercutting of the worm wheel. In the condition of adopting slight modification, this problem can be overcome due to the removal of a part of one sub-conjugate area containing the curvature interference limit line. In order to measure the effect of the avoidance of undercutting, a strategy to determine the meshing point in the most severe condition is proposed for a type II worm drive. The presented strategy can be divided into two steps. The first step is to establish a system of nonlinear equations in five variables in accordance with the theory of gearing. The second step is to solve the procured nonlinear equations by numerical iterative method to ascertain the meshing point required. A numerical example is presented to verify the validity and feasibility of the proposed scheme.