In this paper, a new cooperative fault accommodation algorithm is proposed for multiple-vehicle formation flying missions embedded with absolute measurements. This framework provides two recovery modules, namely a low-level fault recovery (LLFR) module and a formation-level fault recovery (FLFR) module. The framework also includes a high-level (HL) supervisor. In the LLFR module, a conventional recovery controller (RC) based on a given fault severity estimate is employed. In case that the LLFR controller cannot fully recover the faulty vehicle due to an imprecise fault estimate, the error bounds imposed by the mission specifications can be violated and the supervisor identifies this violation and activates the FLFR module. This module is responsible for reconfiguring the weighted absolute measurement formation (WAMF) digraph, applying a robust controller, and imposing constraints on the desired input vectors of the partially LL-recovered vehicle and its neighbor vehicles. Consequently, the formation mission specifications can still be guaranteed so that the fault is cooperatively recovered by our proposed scheme. Simulation results for a satellite formation in planetary orbital environment (POE) confirm the validity and effectiveness of our analytical work.