n this work, the three-dimensional unsteady flow was scrutinized adjacent to a flat plate immersed inside a fluid with electric conductivity in the presence of constant magnetic field. An extended model of group transformation method was exploited, comprising three parameters, to transform the mathematical model into a new system of ordinary differential equations (ODEs). The proposed method is rarely and seldom used in handling higher dimensions coupled equations. Two cases were studied, the stretching and shrinking plate. In the first case, the results showed that both of magnetic parameter, M, and Prandtl number, Pr, affected inversely the fluid velocity, the shear stress and the temperature distribution. On the contrary, the heat flux increased when both M and Pr increase. That could be interpreted by the effect of larger magnetic force and fluid viscosity, respectively. In case of shrinking plate, the attained results were opposite to those of stretching case specially for the effect of magnetic parameter.