In this paper, the flow of hydromagnetic non-Newtonian fluid under couple stresses through a porous channel is investigated using the Eyring--Powell model. The fluid is driven by an axial constant pressure gradient. Approximate solutions of the nonlinear dimensionless equations governing the fluid flow are obtained using a new modification of Adomian decomposition method (ADM). The effects of the variation of various flow parameters on both the velocity and temperature fields are deduced and discussed including surface-fluid interface friction and rate of heat transfer.