Practical information on higher-order correlations in a metallic glass, Ni81B19, is derived from x-ray-absorption near-edge-structure (XANES) data. For the structure of amorphous Ni81B19, a statistical evaluation of XANES calculations revealed that a minority of Ni-Ni-B triangles with peculiar shapes and sizes is to a significant degree responsible for the appearance of the experimental XANES features. The two most relevant types of triangles have one Ni-Ni and one Ni-B distance of about 0.25 nm and 0.20 nm each, identical with the average atomic distances of diffraction data. The second Ni-B distance was found to be sharply defined as 0.195 +/- 0.005 or 0.275 +/- 0.015 nm in either type.