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Privacy-preserving routing is crucial for some ad hoc networks that require stronger privacy protection. A number of schemes have been proposed to protect privacy in ad hoc networks. However, none of these schemes offer complete unlinkability or unobservability property since data packets and control packets are still linkable and distinguishable in these schemes. In this paper, we define stronger privacy requirements regarding privacy-preserving routing in mobile ad hoc networks. Then we propose an unobservable secure routing scheme USOR to offer complete unlinkability and content unobservability for all types of packets. USOR is efficient as it uses a novel combination of group signature and ID-based encryption for route discovery. Security analysis demonstrates that USOR can well protect user privacy against both inside and outside attackers. We implement USOR on ns2, and evaluate its performance by comparing with AODV and MASK. The simulation results show that USOR not only has satisfactory performance compared to AODV, but also achieves stronger privacy protection than existing schemes like MASK.