In the fault recovery problem of distribution network with distribution generators (DG), the method of island partitioning is always adopted without considering network reconfiguration and tie switches. And in the traditional distribution network reconfiguration problem, the radial constraints of the network are necessary to ensure that all loads are powered. In this paper, a fault recovery strategy, which can rationally coordinate the distribution network reconfiguration with isolated island partitioning, is presented. Firstly, load cutting and islanding operation are allowed by modifying the relevant radial constraints in the reconfiguration problem. Then, the 0-1 state variables in the constraint are used to simplify the network model and improve the computing efficiency. Finally, the original nonconvex nonlinear problem is optimized and relaxed to the standard mixed integer second-order cone programming (MISOCP) problem which can be easily solved via commercial solver. The example results prove the effectiveness of the strategy and the superiority and accuracy of the algorithm.