Deadlocks, livelock, congestion and faults are the four most important factors that reduce the NoC routing efficiency {[}1]. This paper proposes a new fully adaptive routing protocol for 2D-mesh NoC. It is inspired from the A-star search algorithm and called HRA (Heuristic based Routing Algorithm). The latter is distributed, congestion-aware and fault-tolerant by using only the local information of each router neighbors. HRA does not use VCs (Virtual Channels) but tries to reduce the risk of deadlock by avoiding the 2-nodes and the 4-nodes loops. Results show that HRA ensures a good reliability rate despite of the presence of many faulty links. In addition, it has interesting latencies values in different NoC sizes.