We study the fair division of indivisible items on complete bipartite graph under weakly lexicographic preferences, which considers vertices as goods to be allocated to n agents, with the requirement that the bundles have to be connected. We prove that for any complete bipartite graph, there exists an instance where no connected EFX allocation can be found. However, for a complete bipartite graph such that the number of vertices on both sides is greater than n, a connected EF1 allocation can always be found.