Abstract: Fault detection and isolation in linear time invariant systems is studied using the time redundancy based parity space approaches. It is pointed out that a given fault at a given time lies in the fixed direction in the parity space. The method for fault isolation is presented by separating this fixed direction from the directions in the parity space of the other factors by using optimal transformation matrices. Simulation experiments show that faults can be detected and isolated when sensors, actuators and components may all have faults and that the system has unknown inputs.