We establish a new condition for global consensus of continuous-time multiagent systems with undirected switching interaction graphs. The condition is strictly weaker than the persistency of excitation, one recently shown in [1], to be necessary and sufficient for global exponential consensus. The price paid for the relaxation of the excitation requirement is twofold; on one hand, we establish only global asymptotic consensus without the "exponential" qualifier. On the other hand, we prove that our condition is not necessary. We also prove in this paper that an additional assumption is needed in [1] to extend the consensus result to the case of negatively weighted edges.