We have prepared (111) Co/Cu multilayers using d.c. magnetron sputtering which exhibit room temperature giant magnetoresistances (GMR) around 65%. These values are similar to the record for this system, but more than 20% higher than those reported by other workers. Such big differences are not fully explained, and have been attributed to difficulties in finding the optimum growth conditions. Here we present results on the effect of annealing one of these very high GMR multilayers. The aims of this study were to relate changes in the multilayer structure to the magnetic properties of the sample and the GMR. By using X-ray characterisation and vibrating sample magnetometer measurements we have found that large changes in the GMR are associated with a reduction in the volume fraction of antiferromagnetic alignment, while there was very little (if any) change in the quality of the layering.