Quickly updating the minimum break point set（MBPS）is one of the key methods of improving the computing speed of on-line coordination during grid topology change.A method for updating the MBPS applicable to arbitrary topology change is proposed.According to the variation characteristic of the simple loop after the line commissioning and outage or bus-tie switch open and close，the evolution law of the break point is deduced.And then the evolution law is transformed to the calculation of the relay incidence matrix.So the MBPS can be fast updated based on this method.At the same time，the method proposed can give the minimum（or minimal）break point set whatever the arbitrary topology change.The500kV network of a provincial grid is used as a case study to verify the correctness and effectiveness of the proposed method.