Traditional multivariate statistical methods, which are often used to monitor stationary processes, are not applicable to nonstationary processes. Cointegration analysis (CA) is considered an effective method to deal with nonstationary variables. If there is a cointegration relationship among the nonstationary series in the system, it indicates that a stable long-term dynamic equilibrium relationship exists among these variables. However, due to the complexity of modern industrial processes, there are nonlinear relations between variables, which are not considered by the traditional linear cointegration theory. Alternating conditional expectation (ACE) can perform nonlinear transformation on these variables to maximize the linear correlation of the transformed variables. It will be helpful to deal with the nonlinear relations by modeling with transformed variables. In this work, a new monitoring strategy based on ACE and CA is proposed. The data are first transformed by an ACE algorithm, CA is performed after that, and then monitoring statistics are calculated to determine whether the system is faulty. The strategy is applied to the monitoring of a simulation case and a catalytic reforming unit in a petrochemical company. The results show that the strategy can realize the monitoring of nonstationary process, with a higher fault detection rate and a lower false alarm rate compared with the monitoring strategy based on traditional cointegration theory.