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In observer-based fault reconstruction, one of the necessary conditions is that the first Markov parameter from the fault to the output must be full rank. This paper seeks to relax that requirement by using multiple sliding mode observers in cascade. Signals from an observer are used as the output of a fictitious system whose input is the fault. Another observer is then designed and implemented for the fictitious system. This process is repeated until the first Markov parameter of the fictitious system with respect to the fault is full rank. The result is that robust fault reconstruction can be carried out for a wider class of systems compared to other works that also seek to relax the requirement of a full rank first Markov parameter. In addition, this paper has also investigated and presented the necessary and sufficient conditions as easily testable conditions, and also the precise number of observers required. A simulation example verifies the effectiveness of the scheme.