It is well known that Foley Sammon transform is a very effective method for feature extraction and that face identification is a typical small sample size problem. In the problems

the dimension of original features is so high that the within class scatter matrix is always singular. In the singulas case

how to calculate Foley Sammon optimal discriminant vectors(FSDV) is a very difficult problem. This paper presents a fast algorithm for calculating FSDV for small sample size problems. The main idea of the proposed algorithm is to map the problem of calculating FSDV in the original feature space to another problem of calculating FSDV in a( c-1 ) dimensional (or less) Euclidean space(where c is the number of pattern classes). In the transformed space

the FSDV can be calculated directly. Generally speaking

the number of classes is much less than the dimension of original sample

so our approach needs less time for feature extraction. We do Experiments on Olivetti Research Laboratory(ORL) face database. The experimental results show that our approach is better than previous method such as Perturbation and Complementary Space in terms of discrimination power and computing time

and also superior to classical "Eigenfaces" and "Fisherfaces" method with respect to recognition rate.