Abstract: The principle and design procedure of unknown input observer schemes for fault diagnosis of dynamic systems are described in this paper. For discrete linear time invariant systems, detailed deduction is given to the algorithm of observer design based on the Kronecker canonical form transformation of matrix pencil. The resulted observer is sensitive to specific faults and is uncoupled from other unknown inputs. Recursively using the above procedure gives a scheme of observers, which realizes the robust fault detection and isolation for dynamic systems. The problems about the method are also discussed.