A novel flat-faced worm gearing is proposed in this paper. The function of undercutting line is well established, as well as the worm helicoid equations and the conjugate condition function of the worm gearing. By virtue of the elimination method, the task of ciphering out the undercutting function with three variables is simplified to solving a nonlinear equation with single variable and solved. The initiating value recognition technique is deployed to estimate the existing of the solutions and afford the rational initiating values for the iterating solving. The numerical results reveal that one undercutting line exists on both sides of single tooth respectively, the undercutting line on the e side is within the inner radius of the flat-faced worm gear, and the undercutting line on the i side is close to the outer radius of the flat-faced worm gear. The possibility of existing the phenomenon of undercutting is higher in the area around the outer radius of the flat-faced worm gear on the i side.