This paper proposes a new system-level application for monitoring out-of-step (OOS) events in power systems. As already known, amplitude-dependent frequency shift is a nonlinear phenomenon of electromechanical oscillations under large disturbances. The frequency shift indicates the system's nearness to instability. This new tool utilizes the Normal Form method to identify the named phenomenon, leading to accelerated OOS detection. The proposed strategy is illustrated and compared to the equal-area criterion method in a single-machine-infinitebus power system. Extensive tests on IEEE 3-and IEEE 50machine power systems prove the efficacy and potential of the proposed method for online warnings of instability and ranking of vulnerable system modes.