A highly reliable and available network which automatically can restore itself from failures is an important concept for the future high capacity broadband networks. Self-healing algorithm, restoring the failed VPs (Virtual Paths) in the backbone ATM networks, is an indispensable technique to meet these requirements. In this paper we propose a coordination-based restoring self-healing algorithm called C-TRUS, which meets different requirements of service classes of survivability by using a simple rerouting and capacity reserving protocols. The simulation results show that the proposed algorithm can restore VPs quickly and improve the restoration time in case of multi-failures by using network resources very efficiently. Furthermore, C-TRUS outperforms the combination method in both restoration ratio and restoration time. In addition, the significant improvement of restoration ratio in the multi-failure scenario has been achieved.