A new FDOs (fault diagnostic observers) and the residual generation schemes using the FDOs are suggested for the process fault detection and isolation of linear (control) systems. The design method of the FDO is described, first, for the full measurement systems. Then it is extended for the systems with unmeasurable state variables. An unknown input observer is proposed and applied for the extension. The size of the observer bank may be the smallest, specially in full measurement systems, because the order of the proposed FDO is very low. In spite of the simplicity, the scheme provides the same information for the detection and isolation of the anticipated faults as the conventional multiple observer based schemes. The residuals may be structured so that fault isolation can be performed by pre-selected logic. An FDIS using the proposed scheme is constructed for the model of the four-tank system. Simulation results show the practical feasibility of the proposed scheme.