Speed and accuracy in classification of electroencephalographic (EEG) signals are key issues in brain computer interface (BCI) technology. In this paper, we propose a fast and accurate classification method for cursor movement imagery EEG data. A two-dimensional feature vector is obtained from coefficients of the second order polynomial applied to signals of only one channel. Then, the features are classified by using the k-nearest neighbor (k-NN) algorithm. We obtained significant improvement for the speed and accuracy of the classification for data set la, which is a typical representative of one kind of BCI competition 2003 data. Compared with the Multiple Layer Perceptron (MLP) and the Support Vector Machine (SVM) algorithms, the k-NN algorithm not only provides better classification accuracy but also needs less training and testing times. (C) 2010 Elsevier B.V. All rights reserved.