We investigate the dynamics of counter-current reacting flow under varying strengths of the counterflow and report the occurrence of global instability phenomena. This clarifies the role of global instability in the transition between attached and lifted flames. The research is performed with the help of the Large Eddy Simulation method using a high-order numerical method. The combustion process is modelled by applying detailed chemical kinetics for hydrogen combustion with chemical reaction terms computed from the resolved scale. The flow configuration consists of a central jet of nitrogen-diluted hydrogen fuel surrounded by an annular nozzle with a suction slot enforcing counterflow in the vicinity of the fuel stream. Suction strength is controlled by the ratio between the velocity in the suction slot (Usuc) and the velocity of the fuel jet (Uj) (I=Usuc/Uj). The Reynolds number based on the fuel parameters and the central nozzle diameter is Re=1600. Two values of the suction strength are considered (I=0.1,0.2) as well as the case without suction (I=0.0). A hot oxidizer (air) provided in the region outside the co-axial nozzle causes fuel auto-ignition far from the injection system after which the flame propagates downstream. It is shown that increasing the suction strength postpones the ignition and shifts its axial location downstream. Depending on the I parameter the flame stabilizes as attached (I=0.0,0.1) or lifted (I=0.2). It is shown that the flames in the cases with I=0.0,0.1 are very similar to each other appearing as laminar non-premixed flames both in the nozzle vicinity and far downstream. The flame in case I=0.2 is turbulent and much more dynamic. Its lifting is the result of global instability appearing at increased suction in the region of counter-current flow. It is shown that the global instability induces strong toroidal vortices that create a premixed reaction zone at the flame base. This flow structuring prevents upstream flame propagation and intensifies the mixing process ensuring almost complete fuel burning in a short distance from the nozzle.