The disclosure proposes a routing message delivery method, a relay node using the same method, and a communication network using the same method. According to one of the exemplary embodiments, the proposed routing message delivery method would include at least but not limited to initiating a timer having a first timer value that is a non-zero positive number, forwarding a first routing message via a first path in response to receiving the first routing message before the timer expires, initiating a second routing message via the first path and a second path in response to not receiving the first routing message before the timer expires, constructing a current network topology, evaluating the first path and the second path within the current network topology, and updating the current network topology.