The purpose of this study is to maintain efficient backup routes for reconstructing overlay trees quickly. In most conventional methods, after a node leaves the trees, its children start searching for a new parent. In this reactive approach, it takes a lot of time to find a new parent. In this paper, we propose a proactive approach to finding a new parent over the overlay trees before the current parent leaves. A proactive approach allows a node to find its new parent immediately and switch to the backup route smoothly. In our proposal, the structure of the overlay tree using a redundant degree can decide a new parent without so much overhead. Simulations demonstrate our proactive approach can recover from node departures 2 times faster than reactive approaches, and can construct overlay trees with lower overheads than another proactive method. Additionally we carried out experiments over actual networks and their results support the effectiveness of our approach. We confirmed that our proposal achieved better streaming quality than conventional approaches.