Large amplitude oscillation shear has been an important method to investigate the yielding and flow behavior of yield stress materials. However, there are great uncertainties in determination of the yield stress from the shear stress (or shear strain) dependence of the apparent dynamic moduli or the relative harmonic intensity using Fourier transform rheology. The yield stress from these dynamic methods is also inconsistent with the steady shear and transient shear measurements. We propose a new method, namely, stress bifurcation, based on the geometric average of elastic and viscous Lissajous curves to study the yielding transition of different yield stress fluids in large amplitude oscillatory shear flow. The results prove that typical yield stress fluids such as concentrated emulsions, polymer nanocomposites, microgels, and particulate gels all exhibit stress bifurcations, both inter and intra cyclically, in large amplitude oscillatory shear experiments. Such stress bifurcation phenomena between the average stress-strain (or strain rate) curves are independent of the type of input signal, i.e., stresscontrolled versus strain-controlled. A start yield stress (strain) (related to strain) and an end yield stress (strain rate) (related to strain rate), instead of a single critical variable, were suggested to characterize yielding transitions. The frequency dependences of critical stresses, critical strain, and critical strain rate determined by the new method were also investigated systematically for the different kinds of yield stress fluids. A visco-elastic-plastic model, the Kelvin-Voigt-Herschel-Bulkley model, was also adopted to understand the stress bifurcation and frequency dependencies of critical variables in large oscillatory shear flow. (C) 2017 The Society of Rheology.