Social conventions have been used as an efficient mechanism to facilitate coordination among agents. Establishing a convention in a decentralised manner has attracted much attention in the literature. Existing techniques on convention emergence are not robust. These techniques may establish sub-conventions under particular network structures. The emergence of sub-conventions indicates that agents in a society fail to conform to a single convention. As a result, the coordination among these agents is negatively affected. In this paper, we propose a strategy to avoid sub-conventions under diverse network structures. The proposed strategy requires agents to only have local views. We prove that a convention can be established using the proposed strategy. We also give empirical studies on the speed of convention emergence with various experimental settings.