The giant magnetostriction observed in rare-earth transition-metal compounds such as Terfenol-D (Tb0.3Dy0.7Fe2) is commonly associated with the huge anisotropy of the 4f electron cloud. We report here the experimental observation of this phenomenon at the atomic scale, in amorphous matter. By using extended x-ray absorption fine structure spectroscopy in a differential mode, the bond strains resulting from the coupling between the anisotropic shape of the Tb 4f charge density and the environment crystalline electric field are measured. In a-TbFe2 we measure Fe-Fe and Fe-Tb bond contractions equal to 6(1)x 10−4 Å and of 9(2) x 10−4 Å, respectively. These are the smallest atomic displacements ever detected in amorphous matter.