The Fault Detection and Isolation (FDI) using the Unknown Input Observer (UIO) for a supermarket refrigeration system is investigated. The original system's state $T_{goods}$ (temp. of the goods) is regarded as a system unknown input in this study, so that the FDI decision is not disturbed by the system uncertainties relevant to this state dynamic and the original system disturbance $Q_{airload}$ (the thermal feature of the air). It has been observed that a single UIO has a very good detection capability for concerned sensor and parametric faults. However, only the parametric fault can be isolated by using a bank of UIOs. Thereby, a complete FDI approach is proposed by combining the Extended-Kalman-Filter (EKF) and UIO methods, after an extensive comparison of KF-, EKF- and UIO-based FDI methods is carried out. The simulation tests show that the complete FDI approach has a good and successful FDI capability regarding to concerned fault scenarios.