H-mode theory (Shaing and Crume Jr 1989 Phys. Rev. Lett. 63 2369) is extended to include realistic effects such as charge-exchange momentum loss and the magnetic stresses. Local critical plasma parameters for the onset of the bifurcation are obtained and can be compared quantitatively with experimental measurements. It is concluded that local critical parameters are more meaningful in quantifying H-mode transition than the global power threshold scaling law.