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Several approaches for IP fast rerouting have been proposed to augment resiliency of IP networks. For example, NotVia uses IP tunnels to avoid failure component, and FIFR prepares two routing tables to switch packets according to incoming interfaces. In this paper, for two-table approach such as FIFR, we propose to use 2-bit marking on packet header to overcome one of the problems called route bouncing. By preventing route bouncing, more efficient use of network resources are possible. We further show that our method not only prevents route bouncing but also prevents packet loops in case of multiple failure. Note that, although multiple failure occurs with low probability, once it occurs network performance significantly degrades since size of loops is far larger than microloops.