Linear discriminant analysis (LDA) is a well-known scheme for feature extraction and dimensionality reduction of labeled data in a vector space. Recently, LDA has been extended to two-dimensional LDA (2DLDA), which is an iterative algorithm for data in matrix representation. In this paper, we propose non-iterative algorithms for 2DLDA. Experimental results show that the non-iterative algorithms achieve competitive recognition rates with the iterative 2DLDA, while they are computationally more efficient than the iterative 2DLDA.