Fault detection filters are a special class of observers that can generate directional residuals for the purpose of fault isolation. This paper proposes a new approach to design robust (in the disturbance de-coupling sense) fault detection filters which ensure that the residual vector, generated by this filter, has both robust and directional properties. This is done by combining the unknown input observer and fault detection filter principles. The paper proposes a new full-order unknown input observer, and gives necessary and sufficient conditions for its existence. After the disturbance de-coupling conditions are satisfied, the remaining design freedom can be used to make the residual have the directional property, based on the fault detection filter principle. A nonlinear jet engine system is used to illustrate the robust fault isolation approach presented. It is shown that linearization errors can be approximately treated as unknown disturbances and be de-coupled in the design of a robust fault detection filter. Simulation results show that mis-isolation of faults can be avoided using the robust scheme.