This technical note focuses on the leader-following output consensus problem for a class of high-order nonlinear multiagent systems under a fixed directed graph. To obtain the global result of output feedback control for the system with the less conservative condition on nonlinear terms than traditional Lipschitz one, the novel reduced-order dynamic compensator is constructed. By introducing an appropriate state transformation, a new fully distributed output feedback controlmethod is proposed, which greatly simplifies the design procedure compared with the backstepping method. The distributed linear-like controller with a dynamic gain is designed for each agent based only on the relative output measurements of neighboring agents. The condition that the orders of all agents should be the same is not needed anymore with the proposed method; thus, the novel result will have extensive applications. Finally, the theoretical results are supported by a numerical simulation.