The cooperative output regulation problem for linear uncertain multi-agent systems was studied in [14] via an internal model approach under the assumption that the information graph of the system contains no cycle. In this technical note, we further show that the no-cycle assumption can be removed if all subsystems of the follower have the same nominal dynamics. Moreover, by directly making use of the property of the internal model, we provide a more straightforward proof than the one in [14] in that we don't need to verify the satisfaction of certain matrix equations.