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The purpose of this paper is to investigate a new method for EEG signals classification. A powerful method for detecting these signals can greatly contribute to areas such as making robotic arms for disabled people, mind reading and lie detection tools. To this end, this study makes two interesting contributions. As a major contribution, a new classifier based on a radial basis function neural network (RBFNN) is presented. As the center determination method of a RBFNN classifier has a high impact on the final classification results, we have adopted Jellyfish search (JS) algorithm for choosing the centers of the Gaussian functions in the hidden layer of the RBFNN classifier. Additionally, Locally Linear Embedding (LLE) technique is investigated for reducing the dimensionality of EEG signals. Two series of various experiments are designed to validate our proposals. In the first set of the experiments, the proposed RBFNN classifier is compared with other state-of-the-art RBFNN classifiers. In the second set of the experiments, the performances of the proposed EEG signals classifications are evaluated on a challenging dataset for EEG signals classification. The experimental results demonstrate the superiority of our proposed method even compared to the methods based on the convolutional neural networks. Supplementary Information The online version contains supplementary material available at 10.1007/s12065-022-00802-2.