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Multilayer Co/Au films were deposited on 40 nm Au underlayer by magnetron sputtering. The Co thickness is kept constant at 0.5 nm while the Au thickness is varied from 0.5 to 8 nm. Magnetic measurements show that the perpendicular anisotropy of the films changes from 3 × 106 to 1.5 × 106 erg/cm3 as the Au thickness changes from 6 to 1 nm. Two films of (Co 0.5 nm/Au 6 nm) × 9/Au 40 nm (denoted Au6) and (Co 0.5 nm/Au 1 nm) × 50/Au 40 nm (denoted Au1) were examined by transmission electron microscopy. For the Au6 film, a bright-field image reveals the curvature of the multilayer. High-resolution electron microscopy shows that the curvature consists of many atomic steps leading to a rough interface. The Au layer has the fcc structure (ABCABC stacking) and the Co layer of two atomic layers interrupts the ABCABC stacking of Au and could be fitted to the AB stacking. In contrast to the Au6 film, the Au layers and the Co layers in the Au1 film cannot be identified in the high-resolution electron microscopy image. Bright field transmission electron microscopy images reveal the evidence of local clustering of Au and Co. A high density of 1/3 a dislocations is observed which supports the clustering argument. The anisotropy of the films is discussed in connection with the observed nanostructure involving the steps and the clustering of Au and Co.