Probabilistic Packet Marking algorithm suggests a methodology to identify all the participated routers of the attack path by probabilistically marking the packets. In this approach, these marked packets contain partial information regarding the routers of the attack path. At receiver, to get the complete information of every router, it requires more number of marked packets and hence more combinations and more false positives. To overcome this drawback we have presented a novel idea in finding the exact IP address of the routers in the attack path by applying Chinese Remainder Theorem. The result of our implementation reveals that our idea requires less number of marked packets and takes no time in constructing the attack path. The same idea is true even in the case of multiple attackers.