In this paper, we propose a nonlinear feature extraction method which is based on centroids and kernel functions. The dimension reducing nonlinear transformation is obtained by implicitly mapping the input data into a feature space using a kernel function, and then finding a linear mapping based on an orthonormal basis of centroids in the feature space that maximally separates the between-class relationship. The proposed method utilizes an efficient algorithm to compute an orthonormal basis of centroids in the feature space transformed by a kernel function and achieves dramatic computational savings. The experimental results demonstrate that our method is capable of extracting non-linear features effectively so that competitive performance of classification can be obtained in the reduced dimensional space.