Recent studies have demonstrated the disassociation between the mu and beta rhythms of electroencephalogram (EEG) during motor imagery tasks. The proposed algorithm in this paper uses a fully data-driven multivariate empirical mode decomposition (MEMD) in order to obtain the mu and beta rhythms from the nonlinear EEG signals. Then, the strong uncorrelating transform complex common spatial patterns (SUTCCSP) algorithm is applied to the rhythms so that the complex data, constructed with the mu and beta rhythms, becomes uncorrelated and its pseudocovariance provides supplementary power difference information between the two rhythms. The extracted features using SUTCCSP that maximize the interclass variances are classified using various classification algorithms for the separation of the left- and right-hand motor imagery EEG acquired from the Physionet database. This paper shows that the supplementary information of the power difference between mu and beta rhythms obtained using SUTCCSP provides an important feature for the classification of the left- and right-hand motor imagery tasks. In addition, MEMD is proved to be a preferred preprocessing method for the nonlinear and nonstationary EEG signals compared to the conventional IIR filtering. Finally, the random forest classifier yielded a high performance for the classification of the motor imagery tasks.