Brain computer interface decodes signals that the human brain generates and uses them to control external devices. The signals that are acquired are classified into movements on the basis of feature vector after being extracted from raw signals. This paper presents a novel method of classification of four finger movements (thumb movement, index finger movement, middle and index finger combined movement and fist movement) of the right hand on the basis of EEG (Electroencephalogram) data of the movements. The data-set was obtained from a right-handed neurologically intact volunteer using a noninvasive BCI (Brain-Computer Interface) system. The signals were obtained using a 14 channel electrode headset. The EEG signals that are obtained are first filtered to retain alpha and beta band (8-30 Hz) as they contain the maximum information of movement. Power Spectral Density (PSD) is used for analysis of the filtered EEG data. Classification of the features is done using various classifiers. Various classifiers have been tested and compared on basis of the mean class accuracy achieved. The classifier chosen for the study is logistic regression, which gives an accuracy of 65%. Other classifiers that were tested were multi-layer perceptron, linear discriminant analysis, and quadratic discriminant analysis. The novelty of this research is the targeted finger movements. These movements were targeted so they can be further used for control of upper limb prosthesis.