Fisher's linear discriminant analysis (FLDA) has been widely used in pattern classification due to its criterion, called Fisher's ratio, based on the ratio of between-class variance to within-class variance. Recently, a linear constrained discriminant analysis (LCDA) was developed for huperspectral image classification where Fisher's ratio was replaced with the ratio of inter-distance to intra-distance and the target signatures were constrained to orthogonal directions. This paper directly extends the FLDA to constrained Fisher's linear discriminant analysiss (CFLDA), which uses Fisher's ratio as a classification criterion. Since CFLDA is supervised which requires a set of training samples, this paper further extends the CFLDA to an unsupervised CFLDA (UCFLDA) by including a new unsupervised training sample generation algorithm to automatically produce a sample pool of training data to be used for CFLDA. In order to determine the number of classes, p, to be classified, a newly developed concept, called virtual dimensionality (VD) is used to estimate the p where a Neyman-Pearson-based eigen-analysis approach developed by Harsanyi, Farrand and Chang, called noise-whitened HFC (NWHFC)'s method, is implemented to find the VD. The experimental results have shown that the proposed UCFLDA perform effectively for HYDICE data and provides a promising unsupervised classification technique for hyperspectral imagery.