Peer-to-Peer (P2P) networks are attracting considerable research interest because of their scalability and high performance relative to cost. One of the important services on a P2P network is the streaming service. However, because each node in the P2P network is autonomous, it is difficult to provide a stable streaming service on the network. Therefore, for a stable streaming service on the P2P network, a fault-tolerant scheme must be provided. In this paper, we propose two new node selection schemes, Playback Node First (PNF) and Playback Node first with Prefetching (PNF-P) that can be used for a service migration-based fault-tolerant streaming service. The proposed schemes exploit the fact that the failure probability of a node currently being served is lower than that of a node not being served. Simulation results show that the proposed schemes outperform traditional node selection schemes.