For a class of multi-agent systems where the control information of neighbor nodes is unknown and only local relative output information is available for each agent, the distributed fault detection problem based on the unknown input observers is investigated in this paper, and the real-time fault detection of agent itself and its neighbors is realized. Firstly, by decomposing and transforming the node dynamics, a reference model for fault detection based on the relative output information is constructed, and the existence of the unknown input observer is proved. Then, the unknown input observer that decoupled from the control information of neighbor nodes is designed, which breaks the limitation that the lack of control information may lead to the failure of the observer. Finally, the fault detection algorithm based on the unknown input observer is designed, and the distributed implementation of the algorithm is achieved. The simulation results validate the effectiveness and improvements of the proposed algorithm.