In recent years， several wide spreading blackouts have been caused by mal-operations of the backup protection that result from the overloading of some transmission lines after one faulted transmission line is tripped. This paper gives a new solution to this problem. A new concept of RCTL（relative cluster of the transmission line） is introduced firstly. Then the method for searching RCTL based on decision tree theory and method for calculating distribution coefficient of RCTL is introduced. On this basis， a new load shedding control strategy for backup protection to prevent cascading outages is proposed. Simulation of CEPRI standard model shows that the new control strategy for backup protection against cascading outages works well.