This paper proposes a new FDI(Fault Detection and Isolation) method, which is called EPSA(Extended Parity Space Approach). This method is particularly suitable for fault detection and isolation of the system with one faulty sensor or two faulty sensors. In the system with two faulty sensors, the fault detection and isolation probability may be decreased when two faults are occurred between the sensors related to the large fault direction angle. Nonetheless, the previously suggested FDI methods to treat the two-faults problem do not consider the effect of the large fault direction angle. In order to solve this problem, this paper analyzes the effect of the large fault direction angle and proposes how to increase the fault detection and isolation probability. For the increase the detection probability, this paper additionally considers the fault type that is not detected because of the cancellation of the fault biases by the large fault direction angle. Also for the increase the isolation probability, this paper suggests the additional isolation procedure in case of two-faults. EPSA helps that the user can know the exact fault situation. The proposed FDI method is verified through Monte Carlo simulation.