The Generalized Likelihood Ratio (GLR) method performs statistical tests on the innovations sequence of a Kalman-Buchy filter state estimator for system failure detection and its identification. However, the major drawback of the conventional GLR is to hypothesize particular failure type in each case. In this paper, a method to solve this drawback is proposed. The improved GLR method is applied to a PWR pressurizer and gives successful results in detection and identification of any failure. Furthermore, some benefit on the processing time per each cycle of failure detection and its identification can be accompanied.