A method for multiple fault diagnosis of plants described by a linear difference model is proposed in the form of an algorithm. The algorithm is based on the observation that, when the number of faulty units of the system is known, the set of faulty units can be differentiated from other sets by checking linear varieties in the measurement data space. It is further shown that the system withtnumber of faults can be diagnosed within (t+1) sample/time units if the input-output measurements are rich and that the algorithm can be used for diagnosis even when the number of faults is not known in advance.