This paper presents some results of magnetoresistance measurements on sputter deposited Co/Cu thin film multilayers. We find that large values of magnetoresistance approaching 40% can be obtained and that these values oscillate in magnitude with the thickness of the non-magnetic spacing layer with a period of about 1.1 nm. It appears that the multilayer must be grown on a particular form of underlayer to realize these large values of magnetoresistance ratio.