The cooperative output regulation problem for linear uncertain multi-agent systems was studied invia 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 inin that we don't need to verify the satisfaction of certain matrix equations.