Because the contact patterns of spiral bevel and hypoid gears are highly sensitive to tooth flank geometry, it is desirable to reduce the flank deviations caused by machine errors and heat treatment deformation. Several methods already proposed for flank correction are based on the cutter parameters, machine settings, and kinematical flank motion parameters of a cradle-type universal generator, which are modulated according to the measured flank topographic deviations. However, because of the recently developed six-axis Cartesian-type computer numerical control (CNC) hypoid generator, both face-milling and face-hobbing cutting methods can be implemented on the same machine using a corresponding cutter head and NC code. Nevertheless, the machine settings and flank corrections of most commercial Cartesian-type machines are still translated from the virtual cradle-type universal hypoid generator. In contrast, this paper proposes a flank-correction methodology derived directly from the six-axis Cartesian-type CNC hypoid generator in which high-order correction is easily achieved through direct control of the CNC axis motion. The validity of this flank-correction method is demonstrated using a numerical example of Oerlikon Spirac face-hobbing hypoid gears made by the proposed Cartesian-type CNC machine.