The Network-on-Chip (NoC) is limited by the reliability constraint, which impels us to exploit the fault-tolerant routing. Generally, there are two main design objectives: tolerating more faults and achieving high network performance. To this end, we propose a new multiple-round dimension-order routing (NMR-DOR). Unlike existing solutions, besides the intermediate nodes inter virtual channels (VCs), some turn-legally intermediate nodes inside each VC are also utilized. Hence, more faults are tolerated by those new introduced intermediate nodes without adding extra VCs. Furthermore, unlike the previous solutions where some VCs are prioritized, the NMR-DOR provides a more flexible manner to evenly distribute packets among different VCs. With extensive simulations, we prove that the NMR-DOR maximally saves more than 90% unreachable node pairs blocked by faults in previous solutions, and significantly reduces the packet latency compared with existing solutions.