This paper addresses the problem of developing an efficient fault-tolerant routing method for 2D mesh Network-on-Chips (NoCs) to realize dependable and high performance many core systems. Existing fault-tolerant routing methods have two critical problems of high communication latency and low node utilization. Unlike almost all existing methods where packets always detour faulty nodes, we propose a novel and unique approach that packets can pass through faulty nodes. For this approach, we enhance the common NoC architecture by adding switches and links around each node and propose a fault-tolerant routing method with no virtual channels based on the well-known simple XY routing method. Simulation results show that the proposed method reduces average communication latency by about 97.1% compared with the existing method, without sacrificing fault-free nodes.