Partial least-squares (PLS) method has been widely used in multivariate statistical process monitoring field. The goal of traditional PLS is to find the multidimensional directions in the measurement-variable and quality-variable spaces that have the maximum covariances. Therefore, PLS method relies on the second-order statistics of covariance only but does not takes into account the higher-order statistics that may involve certain key features of non-Gaussian processes. Moreover, the derivations of control limits for T-2 and squared prediction error (SPE) indices in PLS-based monitoring method are based on the assumption that the process data follow a multivariate Gaussian distribution approximately. Meanwhile, independent component analysis (ICA) approach has recently been developed for process monitoring, where the goal is to find the independent components (ICs) that are assumed to be non-Gaussian and mutually independent by means of maximizing the high-order statistics such as negentropy instead of the second-order statistics including variance and covariance. Nevertheless, the IC directions do not take into account the contributions from quality variables and, thus, ICA may not work well for process monitoring in the situations when the quality variables have strong influence on process operations. To capture the non-Gaussian relationships between process measurement and quality variables, a novel projection-based monitoring method termed as quality relevant non-Gaussian latent subspace projection (QNGLSP) approach is proposed in this article. This new technique searches for the feature directions within the measurement-variable and quality-variable spaces concurrently so that the two sets of feature directions or subspaces have the maximized multidimensional mutual information. Further, the new monitoring indices including I-2 and SPE statistics are developed for quality relevant fault detection of non-Gaussian processes. The proposed QNGLSP approach is applied to the Tennessee Eastman Chemical process and the process monitoring results of the present method are demonstrated to be superior to those of the PLS-based monitoring method. (c) 2013 American Institute of Chemical Engineers AIChE J 60: 485-499, 2014