Brain computer interface (BCI) allows people to communicate with machines without the use of muscle systems. Although there are various kind of techniques to understand intend of the BCI user, electroencephalography (EEG) is the most popular, practical and widely implemented one. The performance of the EEG based BCI highly depends on extracting effective features. However, there is no a general feature extraction method which provides satisfied performance for all various kind of BCI applications. Therefore, it is very valuable to develop a new feature extraction method. In this paper, we proposed a novel Fast Walsh Hadamard Transform based feature extraction method for classification of EEG signals recorded during right/left hand movement imagery. It does not only provide well-discriminative attributes but also the computational time of extracting the features from a single EEG trial is fast. The proposed method was successfully applied to Data Set III of BCI competition 2003, and achieved a classification accuracy of 88.87% on the test data. The obtained satisfactory results proved that this method can be a successful alternative to the existing feature extraction methods.