Gnutella is a fully decentralized and unstructured peer-to-peer network. It uses the message broadcasting mechanism of flooding. However, while bringing Gnutella network the characters of high degree of robustness and dynamic, this broadcasting mechanism makes the network give redundant messages that increase exponentially. On basis of resolving Gnutella network message broadcasting mechanism, the paper points out the necessity and feasibility of Gnutella network losing contact, and then bring forward the means which can compartmentalize Gnutella network messages PRI according to the transmitting bandwidth, the time, and the resources which are consumed by servents dealing with all kinds of messages. F-Measure is introduced to connection management, which is usually used to evaluate the performance of searching engine. The paper provides a discarding connection management algorithm, which discards the redundant connection by computation and ensures the maximal attainability of message simultaneously. Finally, the arithmetic example and discussion are given.