The extraction of distinctly separable features from electroencephalogram (EEG) is one of the main challenges in designing a brain–computer interface (BCI). Existing feature extraction techniques for a BCI are mostly developed based on traditional signal processing techniques assuming that the signal is Gaussian and has linear characteristics. But the motor imagery (MI)-related EEG signals are highly non-Gaussian, non-stationary and have nonlinear dynamic characteristics. This paper proposes an advanced, robust but simple feature extraction technique for a MI-related BCI. The technique uses one of the higher order statistics methods, the bispectrum, and extracts the features of nonlinear interactions over several frequency components in MI-related EEG signals. Along with a linear discriminant analysis classifier, the proposed technique has been used to design an MI-based BCI. Three performance measures, classification accuracy, mutual information and Cohen's kappa have been evaluated and compared with a BCI using a contemporary power spectral density-based feature extraction technique. It is observed that the proposed technique extracts nearly recording-session-independent distinct features resulting in significantly much higher and consistent MI task detection accuracy and Cohen's kappa. It is therefore concluded that the bispectrum-based feature extraction is a promising technique for detecting different brain states.