The long-wave perturbation method is employed to investigate the hydromagnetic stability of a thin electrically-conductive pseudoplastic
liquid film flowing down the surface of a vertical wall in a magnetic field.The validity of the numerical results is improved through the introduction of the flow index and the magnetic force into the governing equation. In contrast to most previous studies presented in the literature, the solution scheme employed in this study is based on a numerical approximation approach rather than an analytical method. The normal mode approach is used to analyze the stability of the film flow. The modeling results reveal that the flow stability can be enhanced by increasing the intensity of the magnetic field and the flow index, respectively. In general, the instability state can be neutralized through an appropriate control of the applied magnetic field.