Linear discriminant analysis is one of method frequently used and developed in the field of pattern recognition. This method tries to find the optimal subspace by maximizing the Fisher Criterion. Application of pattern recognition in highdimensional data and the less number of training samples cause singular within-class distribution matrix. In this paper, we developed Linear Discriminant Analysis method using Fukunaga Koontz Transformation approach to meet the needs of the nonsingular within-class distribution matrix. Based on Fukunaga Koontz Transformation, the entire space of data is decomposed into four subspaces with different discriminant ability (measured by the ratio of eigenvalue). Maximum Fisher Criterion can be identified by linking the ratio of eigenvalue and generalized eigenvalue. Next, this paper will introduce a new method called complex discriminant analysis by transforming the data into intraclass and extraclass then maximize their Bhattacharyya distance. This method is more efficient because it can work even though within-class distribution matrix is singular and between-class distribution matrix is zero.