The determination of the break point set（BPS） of a relay is the key to directional protective relays coordination in a large-scale multi-loop power network. This paper transforms the determination of BPS to seek the feedback arc set（FAS） into a directed graph. Through a study of the characteristics of FAS， a new practical method for fast acquisition of FAS is developed and adopted to heuristically search for the functional dependency set of the relays that have primary/backup coordinative relations in a power network. In this way， the irrational searching start points and repeated loops can be removed， and the BPS of any relay is quickly determined. When the topology of power network changed， only the functional dependencies of a relative relay need to be modified and the new BPS can be quickly determined based on the original search results. The test results of an illustrative multi-loop network show that the new method is valid.