The focus in this paper is on active fault detection (AFD) for MIMO systems with parametric faults. The problem of design of auxiliary inputs with respect to detection of parametric faults is investigated. An analysis of the design of auxiliary inputs is given based on analytic transfer functions from auxiliary input to residual outputs. The analysis is based on a singular value decomposition of these transfer functions Based on this analysis, it is possible to design auxiliary input as well as design of the associated residual vector with respect to every single parametric fault in the system such that it is possible to detect these faults.