Series braking resistors (SeBR) offer an effective way to enhance transient stability for severe near-to-generator faults cleared with a delay. The SeBR is switched on for a short time, already during the fault. The SeBR should switch on as quickly as possible after identifying the risk of losing transient stability. Then, the SeBR is switched off, and it is the decision-making algorithm that chooses the switch-off time. This paper presents an algorithm to choose the moment the SeBR switches off. The algorithm identifies the direction of a rotor motion based on changes in the square of the current and real power of the synchronous machine. The proposed algorithm is characterized by its simplicity, and is easy to implement because it uses local measurements. To develop the control algorithm, the effect of the SeBR on power angle characteristics for a fault state and post-fault states were determined. In addition, the effect of the SeBR on transient stability is explained using the equal area method. The conducted simulation tests have confirmed that the proposed SeBR control algorithm leads to longer critical clearing times, and thus it contributes to enhanced transient stability.