This paper addresses a method for fault detection (FD) by maximizing the fault to residual sensitivity. It uses the newly developed ℋ− index properties and minimizing the well known ℋ∞ norm for worst case disturbance attenuation. The fault detection problem is formulated as LMI feasibility problem in which a cost function is minimized subject to LMI constraints. This objective is coupled to a transient response specification expressed by eigenvalue assignment formulation. This approach is then studied for both proper and strictly proper systems. Sufficient conditions are also given to enhance the disturbance decoupling. The effectiveness of the proposed approach is shown by a numerical example