We studied spin-dependent electron transport in noncollinear magnetic multilayers Co/Cu/Co by using the Boltzmann equation in the layer-by-layer approach. Without a priori set the transverse part of the spinor distributions to zero in the ferromagnetic layers and by adopting new mechanism for the “injection” of these components in the magnetic layers, we have been able to achieve a steady state for the spin current across the noncollinear multilayer in which the spin current continuously changes its direction over a distance given by a new transport length scale, which is about 3nm for a typical ferromagnetic 3d transition-metal such as Co. This has a direct impact on the thickness dependence of the spin torque in a thin magnetic layer. Furthermore, our theory always obtain a lower resistance of noncollinear magnetic multilayer and a enhanced spin torque about 50% greater for the same amount of electrical energy at particular angle. Finally, we have used the time dependent spin diffusion equation, to study the time evolution of spin torque, and find it achieves its steady state in about 75 femtoseconds after undergoing damped oscillation with a period of about 5 femtosecond.