Residuals in fault detection and diagnosis are usually designed with directional or structured properties to facilitate fault isolation. With directional residuals, best isolation is achieved if the residual directions are orthogonal. In the presence of noise, the residuals are subjected to statistical testing. Testing conditions are ideal if the Fisher information matrix of the residuals is diagonal. In this paper, we introduce a design technique which, subject to certain restrictions, provides orthogonal directions and diagonal information matrix simultaneously.