In the coordination and setting of relay protection for the complex ring-network， selecting the minimum break point set（MBPS） is almost sure to have several identical cardinal MBPSs. This paper presents a method for selecting optimum MBPS from Multi-MBPSs with the same cardinal number， which takes into account the nodes and linesimpact on the vulnerability of breakpoints comprehensively， then proposes conception of indicator of relays vulnerability. Finally， the feasibility and effectiveness of the method proposed is proven with the example of simulation.