This paper addresses the observability problem of 2D Multiple Autonomous Underwater Vehicles (MAUVs) cooperative navigation system. We derive the conditions to keep the local weak observability of navigation system using the Lie derivatives, and characterize the unobservable trajectories of AUVs. We design a series of simulation experiments using the Extended Kalman Filter (EKF) to verify the theoretical results. Finally, the simulation results show that the good performance of navigation system can be presented if avoiding the unobservable trajectories of AUVs.