The problem of fault diagnosis is researched for linear discrete-time systems with delayed measurements. A delay-free transformation approach for delayed measurements is proposed, and a reduced-order observer-based fault diagnosis approach is presented, which needn’t residual to embody faults. Firstly, by constructing an augmented system which comprises the faults’ states and doing the delay-free transformation of the delayed measurements, the problem of fault diagnosis for time-delay systems is transformed into the problem of state observation for a delay-free augmented system. Then, the design approach of a fault diagnoser is given which makes the diagnosis error of the fault diagnoser approach to zero at the preseted exponential rate. Simulation results show the feasibility and effectiveness of the proposed approach.