Linear discriminant analysis (LDA) is designed to seek a linear transformation that projects a data set into a lower-dimensional feature space for maximum class geometrical separability. LDA cannot always guarantee better classification accuracy, since its formulation is not in light of the properties of the classifiers, such as the automatic speech recognizer (ASR). In this paper, the relationship between the empirical classification error rates and the Mahalanobis distances of the respective class pairs of speech features is investigated, and based on this, a novel reformulation of the LDA criterion, distance-error coupled LDA (DE-LDA), is proposed. One notable characteristic of DE-LDA is that it can modulate the contribution on the between-class scatter from each class pair through the use of an empirical error function, while preserving the lightweight solvability of LDA. Experiment results seem to demonstrate that DE-LDA yields moderate improvements over LDA on the LVCSR task.