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Complex system exists extensively in modern process manufacturing industry. One major problem of its fault diagnosis is how to extract the inner partial relationship, with which we can model the fault performance and then identify the faults. In this paper, based on Generalized Linear Model (GLM), an improved CCA algorithm (GLCCA) is proposed to extract both the linear and nonlinear relationship in the complex system. A pneumatic experiment table as a complex system with some fault simulation is obtained from the state key laboratory. The data is composed of the pressure signature of six reducing valves and the signature of another four unit state. Simulated and experimental results show that this method is adequate enough to extract the inner relationship in the complex system.