The giant magnetoresistance (GMR) was measured for Fe/Au magnetic multilayers in both the CIP and CPP configurations, for a series of samples each having the same thickness for the Fe layers (10 Å) but a different thickness for the Au layers (in the range 20-50 Å). It was found that the GMR is only a few per cent in the CIP configuration, whereas the GMR ranges from 20 to 80% in the CPP configuration. We attribute this order-of-magnitude difference in the values of the GMR for the two configurations to the short electron mean free path, resulting from the relatively high resistivity of these multilayers. A short electron mean free path reduces sharply the value of the GMR in the CIP configuration, while leaving unchanged the value of the GMR in the CPP configuration.