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Electron holography in a transmission electron microscope was applied to measure the phase shift induced by Au clusters as a function of the cluster size. Large phase shifts Df observed for small Au clusters cannot be described by the well-known equation Df=C_E V_0 t (C_E: interaction constant, V_0: mean inner Coulomb potential (MIP) of bulk gold, t: cluster thickness). The rapid increase of the Au MIP with decreasing cluster size derived from Df, can be explained by the compressive strain of surface atoms in the cluster.