We propose a novel method for extracting a rhythmically oscillating signal from EEG recordings including multiple source signals which have similar frequencies. The main application of this method is brain computer interfaces (BCI), which use rhythmically oscillating signals such as alpha, mu, and beta waves, as feature signals. It is difficult to separate those components and/or extract an command-related component when these feature signals span the same frequency band. The main idea is to assume that signals generated in different brain parts have different phases, even though they have the same frequency. This hypothesis is effectively incorporated with the previously proposed rhythmic component extraction (RCE) method, which successfully extracts a signal oscillating at a certain frequency from multi-channel sensor signals in the BCI application. The signal model is firstly given and then this novel extraction method is formulated as an optimization problem. We apply the proposed method for the classification of multi-channel EEG signals between imaginary left/right hand movement. Our experiment suggests that the proposed method is effective in feature extraction for motor-imagery based BCI.