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Routing in intermittently connected mobile ad hoc networks (ICMAN) is particularly challenging due to intermittent connectivity and unstable topology. To deal with this problem, researchers have proposed some routing schemes based on message relay. Proposed efforts focus on the tradeoff between average message delivery delay and communication overhead. However, message delivery with a certain probability of bounded delay, rather than average delay, is more practical in real world scenario. In this paper, we introduce a new routing scheme that can guarantee the bounded delivery delay with a certain probability in random way models. We study the relationship between the probability of bounded delivery delay and the chosen nodes for forwarding. In our scheme, each message is labeled with an expected probability of bounded delivery delay. The fields of messages are updated each time message relay happens. The total number of nodes used for delivery depends on the delivery probability and delay. It is designed to provide bounded end-to-end delay with a certain probability compared with other bounded average delay schemes. The simulation results show that our novel scheme requires less resource than epidemic routing, while provides similar performance.