In a mobile ad hoc network we consider the problem of designing a reputation system that allows to update and to propagate the computed reputation scores while tolerating Byzantine failures. Each time a correct node uses directly a service, it can determine by itself the quality of service currently provided. This fresh and valid rating information is broadcast immediately to all its current neighbors. Then, while the mobile node moves, it can receive from other nodes other recommendations also related to the same service. Thus it updates continuously its own opinion. Meanwhile it continues to broadcast this updated information. The freshness and the validity of the received/sent information become questionable. We propose a protocol that allows a node to ignore a second hand information when this information is not fresh or not valid. In particular, fake values provided by Byzantine nodes are eliminated when they are not consistent with those gathered from correct nodes. When the quality of service stabilizes, the correct nodes are supposed to provide quite similar recommendations. In this case, we demonstrate that the proposed protocol ensures convergence to a range of possible reputation scores if a necessary condition is satisfied by the mobile nodes. Simulations are conducted in random mobility scenarios. The results show that our algorithm has a better performance than typical methods proposed in previous works.