We present an experimental investigation of an original configuration where the laminar flame shape bifurcates when submitted to flowrate modulations. This combustor burns a gaseous methane-air mixture injected vertically in a downward direction. The global equivalence ratio is equal to 0.91, the overall heat release of around 800 W. By increasing the frequency of the mass flow rate modulation from 70Hz to 85Hz, the flame bifurcates from an anchored flame into a lifted flame. The precise switch frequency depends on temperature and flow rates. Some forcing cases lead to bi-stable flames presenting a random transition between the two shapes for a given mass flow rate and modulation frequency. Experimental data stand on high-speed optical diagnostics processed with optical flow and orthogonal decompositions. POD-based analysis reveals different dynamics depending on the flame's average position, particularly a transverse flow motion for detached flames.