This note develops a discrete-time predictor feedback control scheme for continuous-time multiagent systems with input and communication time delays. With measurement of locally available relative state signals among neighbored agents, the controller is able to achieve consensus for a large variety of linear open-loop agent dynamics, including exponentially unstable systems. Moreover, the new design can deal with arbitrarily large time delays in some special scenarios. The feature of discrete-time and relative state measurement substantially saves implementation cost compared with the existing methods in the literature. Numerical simulation demonstrates the effectiveness of the proposed theoretical design.