Recently overlay multicast has become one of the hot issues on multicast research, as it is more flexible than IP multicast and can facilitate application-specific optimization. However, the intermediate nodes in overlay multicast are easier to be faulted compared to those in IP multicast. So it is significant to design an efficient topology maintenance algorithm in overlay multicast, especially for the live streaming media applications. In this paper, the degree and delay constrained topology maintenance problem is studied, and a novel distributed multicast tree reconstruction algorithm called LOcal Topology maintenance Algorithm (LOTA) is proposed. By adopting the active strategy and avoiding package duplicates, LOTA triggers nodes pre-calculate a backup parent periodically before the multicast tree splits rather than letting downstream nodes find a new parent after a node's departure. When a node which is neither root nor leaf is gone, all its children can interact with their respective backup parents to restore the tree immediately in order to enhance the reconstruction performance and save the system maintenance cost effectively. The results of simulation and experiment show that, in both the small-scale and the large-scale group, LOTA's efficiency of tree reconstruction is much higher than the passive strategies, and its control overhead is comparatively low. Therefore, the algorithm is quite suitable for the real-time streaming media applications.