A tight-binding equation of motion ͑EOM͒ method for the simulation of electronic transport in complex, and inhomogeneous systems is presented. Conductance is calculated in the linear response regime where chemical potentials can mimic electrochemical potentials. The technique is first elucidated by application to several simple systems to clarify important issues. A calculation of current-perpendicular-to-the-plane giant magnetoresistance ͑GMR͒ in a Co/ Cu multilayer then follows. A 67% GMR is calculated which originates primarily from spin-dependent interface resistances. The advantages of an EOM method are that complicated geometries can be considered, and interactions such as spin-orbit effects or phonons, for example, may be included easily.