A novel algorithm for making the combination of outputs in the output zero direction of the plant always equal to zero was formulated. Using this algorithm and the result of MacFarlane and Karcanias, a fault detection scheme was proposed which utilizes the directional property of the multivariable linear system. The fault detection scheme is applicable to linear multivariable systems. Results were obtained for both continuous and discrete linear multivariable systems. A quadruple tank system was used to illustrate the results. The results were further verified by the steady state analysis of the plant.