This paper presents a method of removing the noise caused by eye blinks from an electroencephalogram (EEG) signal in real time based on morphological component analysis (MCA). This method sparsely represents both the eye blink and the EEG signal basis matrices using a Short Time Fourier Transform (STFT). This approach has two main advantages: 1) fast computation of the estimation of the signal coefficients using the basis pursuit algorithm 2) less memory requirement. The obtained result shows that the correlation coefficient between the raw EEG and the cleaned EEG is between 0.72 and 0.94 which implies that it is possible to remove eye blink noise from the EEG signal in real time without affecting an underlying brain signal.