Linear discriminant analysis (LDA) has been widely used to extract features to solve various machine learning problems. However, the current LDA methods can be confused by highly dispersed samples. To address this problem, we develop a new LDA method based on a new expression of the theoretical error in classification. The method first combines different class distributions and then constructs the projection matrix on the basis of the statistics of the combined distribution. This is very different from conventional methods that estimate the statistics from individual classes first. The statistics are then combined to construct the projection matrix. The merit of the proposed approach is that it selects discriminant pairs of the combined distribution and discards the scatter structure caused by the dispersed samples. The statistics of this trimmed distribution are less sensitive to the dispersed samples and produce a robust projection matrix. The pairs are selected by a trimming model. The solution is obtained by the alternating direction method of multipliers (ADMM). The proposed LDA method is compared with 17 other LDA methods over 13 datasets belonging to the UC Irvine (UCI) repository, the knowledge extraction based on evolutionary learning (KEEL) repository, and publicly available image websites with different numbers of training samples. The experimental results indicate that the proposed method outperforms the existing methods in many cases.