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The ABR point-to-multipoint connection is now playing a more important role than before. Many consolidation algorithms have been proposed to solve the consolidation noise problem and the slow transient response problem. But few timeout algorithms are proposed to handle the non-responsive branches for the multicast connections. Chen's algorithm needs exchanging control messages between switches . Besides, it may mistake a responsive branch as a non-responsive branch because of fast changes in source rates, which causes wrong information in BRM cells and may lead to network congestion and data losses in the responsive branch. We propose a simple timeout algorithm which can handle the non-responsive branches without exchanging message between switches. The timeout value for each switch is computed locally. Simulation results show that the proposed timeout algorithm can efficiently handle the non-responsive branches and utilize the available bandwidth within a small period of time. In addition, our algorithm could handle the situation when the source rates change quickly.