This paper proposes a new event-based logic of the breaker failure protection to improve power system transient stability by shortening the total clearing time of extreme contingencies involving circuit breaker failures. Stability improvement is achieved by using dual-timer protection with shorter safety margin for multi-phase faults close to the power plant and longer safety margin for remote multi-phase faults and single-phase faults. The use of the output signal obtained for a short safety margin depends on how the substation is configured. In the breaker-and-a-half configuration, this output signal is used to speed up the opening of all adjacent circuit breakers. In substations with the dual (or triple) busbar configuration the output signal obtained with a short safety margin is used to speed up the busbar splitting. A case study was performed for a real large-scale power system. Simulation results confirmed the advantages of the proposed logic. Breaker failure protection with the proposed logic has been implemented in a substation of a large power plant.