<p>This paper presents a novel method for blind source separation of non-Gaussian signals from instantaneous linear mixtures. The approach analytically derives optimal rotation angles to ensure statistical independence among the signals. The process begins by decorrelating the mixed signals, followed by maximizing the kurtosis of the orthogonal signal pairs. By utilizing a sinusoidal objective function, this method calculates the necessary phase shifts, facilitating precise source recovery with minimal computational effort and requiring only four angle tests per signal pair per iteration. The simulation results validate the high accuracy and rapid convergence of the method, even under noisy conditions and scenarios with limited data availability. Compared with traditional optimization techniques, this approach substantially reduces computational complexity, underscoring its superior efficiency. Additionally, the proposed method is evaluated against widely recognized techniques, known for their robustness and execution speed, demonstrating comparable results and performance while maintaining its reliability and efficiency.</p>