Investigate the symmetry-breaking flow bifurcation phenomena and its control of an electrically conducting generalized Newtonian liquids flowing through symmetric sudden expansion channel by applied magnetic field in the transverse direction studied in this paper. The governing nonlinear magnetohydrodynamic equations simplified for low conducting liquid metals are written and solved numerically using PISO-GNFMHD algorithm, which was developed by the author to include generalized Newtonian fluids, as well as the effects of the magnetic field on the fluid flow based on the finite volume method. The effects of non-Newtonian rheology and the magnetic force on flow bifurcation and separation are studied. In case of power-law fluid model the flow transition depends nonlinearly on shear viscosity in particular the shear-thickening fluids delay the onset of bifurcation where as shear-thinning fluids the early flow transition is occurred. The magnetic force is always delay this transition. The main conclusion is the possibility to control the phenomenon of bifurcation finally by applying an external magnetic field.