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The consensus problem is investigated in this paper for a class of multi-agent systems with general linear node dynamics and directed communication topology. A new distributed observer-type consensus protocol designed based only on the relative output measurements of neighboring agents is introduced. Compared with some existing observer-type protocols, the protocol presented in this paper without involving the relative states of observers. By using tools from small gain theory and matrix analysis, some sufficient conditions are obtained to guarantee the achievement of consensus in linear multi-agent dynamical systems where the underlying topology only contains some directed spanning trees. Finally, some numerical simulations are performed to show the effectiveness of the theoretical results.