This paper proposes an online sparse optimization algorithm for fault isolation, which is of a great demand to ensure the normal operation of industrial processes. The proposed method can identify faulty variables without resorting to the historical normal process data. The task of faulty variable location is achieved via performing a sparse matrix decomposition technique on the streaming faulty data, from which a sparse matrix containing fault information is generated and can be further used for pinpointing faulty variables. Additionally, given that process characteristics will change as time goes by, the above decomposition is realized in an online recursive fashion. The efficacy of the proposed method is verified by the Tennessee Eastman benchmark process.