In 2002, Yang and Shy reported a global quenching (GQ) criterion of premixed CH4 flames by turbulence characterized by a Karlovitz number (Ka) estimated at reactant temperature and an equivalence ratio (phi). This article re-analyzes such criteria based on a modified Ka estimated at mean temperature of reactants and products together with newly obtained GQ data at even higher Ka. This modified criterion is compared with a recently found ignition transition, which are then used to evaluate the boundary of thin and broken RZ regimes (Ka = 100) proposed by Peters (2000). It is found that flame GQ occurs beyond the broken RZ regime, where critical Ka >= 100 at 0.6 <= phi < 1.3 forms a parabolic curve with the maximum Ka(c) approximate to 365 occurring possibly near phi = 1, except for very rich flames where Ka(c) = 28 at phi = 1.45. A simple model is proposed to explain these results.