Electroencephalogram (EEG) extraction has widely used Stone's Blind Source Separation (Stone's BSS) algorithm. However, Stone's BSS algorithm is sensitive to the initial half-life (ℎlong, ℎshort) and weight vector W parameters, which affect the convergence of the algorithm. This paper proposes a hybridization of Stone's BSS with Particle Swarm Optimization (PSO) to boost the separation process. An improved Stone's BSS (ISBSS) method is employed to reject eye blinking from the electroencephalogram (EEG) mixture. The electroencephalogram (EEG) mixed-signal is first centralized and whitened; then, it is incorporated into the particle swarm optimization (PSO) iterative algorithm to process the initial (ℎlong, ℎshort) and generate the weight vector W parameters randomly. Finally, the generalized eigenvalue decomposition (GEVD) method is applied to extract EEG singles to obtain a clean EEG signal. A clinical EEG database is used to test the improved and other algorithms. The GEVD method estimates the measurement performance of the proposed algorithm using a carrier-to-interference ratio and integral square error and compares the proposed algorithm with the conventional Stone's BSS, fast independent component analysis (FastICA), evolutionary fast independent component analysis (EFICA), and joint approximate diagonalization of eigen matrices (JADE) algorithms to check its effectiveness. The results show that the suggested hybrid method has a better performance and decreasing elapsed time than conventional Stone's BSS and other algorithms.