Flow-Aware Multi-Topology Adaptive Routing is a new proposal which provides multipath transmissions in the networks based on any IP routing protocol. However, due to utilization of flow tables which store flow forwarding information, it suffers from routing instability and the occurrence of failures. This problem is solved by the mechanism proposed in this letter. The mechanism is based on a Time-To-Live field from the IP protocol header. The mechanism is simple, yet very effective. The evaluation shows that at the cost of additional operations performed by routers the problem is completely eliminated.