In this paper, the authors deal with the problem of diagnosis of multiple sequential faults using statistical test GLR. Based on the work of Willsky and Jones , they propose a modified Generalized Likelihood Ratio (GLR) test, allowing detection, isolation and estimation of multiple sequential faults. Their contribution aims to maximise the rate of good decision of fault detection, using another updating strategy. This is based on a reference model updated on line after each detection and isolation of one jump. To reduce the computational requirement, the passive GLR test will be derived from a state estimator designed on a fixed reference model directly sensitive to system changes.