Although nodes in peer-to-peer networks are viewed as equal entities in function, some of them have much more importance than others in the aspect of overlay topology. This paper introduces the concept of "partition node" to describe the topologically-critical nodes, whose failure may potentially lead to overlay partitioning. Then a simple, effective and distributed method to detect and avoid partition nodes, is proposed. The results of simulation show that the proposed method can optimize the overlay topology and remarkably improve the fault tolerance of unstructured P2P systems under a dynamic environment.