We study the effect on CPP GMR of changing the order of the layers in a multilayer. Using a tight-binding simple cubic two band model (s-d), magneto-transport properties are calculated in the zero-temperature, zero-bias limit, within the Landauer-Büttiker formalism. We demonstrate that for layers of different thicknesses formed from a single magnetic metal and multilayers formed from two magnetic metals, the GMR ratio and its dependence on disorder is sensitive to the order of the layers. This effect disappears in the limit of large disorder, where the results of the widely-used Boltzmann approach to transport are restored.