The objective of this paper is to design a robust fault detection scheme for nonlinear systems. A novel procedure for the design of a nonlinear unknown input observer (UIO) is proposed. The basic principle of unknown input observers is to decouple disturbances from the state estimation error. In the proposed method, the linear UIO design algorithm is extended to nonlinear systems and then observer gain is obtained using unscented transformation (UT). To illustrate the efficiency of the proposed method, it is adopted to detect sensor faults of a highly nonlinear dynamic system. The faulty behavior of output sensors in a jacketed continuous stirred tank reactor (CSTR) is investigated. A single full-order observer is designed to detect sensor faults in the presence of unknown inputs (disturbances). Simulation results show that disturbances and, therefore, a certain degree of model uncertainties can be distinguished from a response to a sensor fault.