Applications such as face recognition that deal with high-dimensional data need a mapping technique that introduces representation of low-dimensional features with enhanced discriminatory power and a proper classifier, able to classify those complex features. Most of traditional Linear Discriminant Analysis suffer from the disadvantage that their optimality criteria are not directly related to the classification ability of the obtained feature representation. Moreover, their classification accuracy is affected by the "small sample size" problem which is often encountered in FR tasks. In this short paper, we combine nonlinear kernel based mapping of data called KDDA with Support Vector machine classifier to deal with both of the shortcomings in an efficient and cost effective manner. The proposed here method is compared, in terms of classification accuracy, to other commonly used FR methods on UMIST face database. Results indicate that the performance of the proposed method is overall superior to those of traditional FR approaches, such as the Eigenfaces, Fisherfaces, and D-LDA methods and traditional linear classifiers.