We report x-ray, EXAFS and neutron diffraction experiments on stress-relieved (SR) and field-annealed (FA) ribbons of Fe78Si9B13 using optimized geometries to measure the structural and magnetic anisotropy to unprecedented accuracy. A peak of magnitude similar to 5% of the main peak height is found in the Delta S(Q) pattern from three independent neutron experiments on the FA ribbons, at Q similar to 3 Angstrom(-1). We establish that this peak is of magnetic origin, arising from moments that to some extent lie perpendicularly to the anneal field direction, and is associated with local structure. We show that this anistropy is consistent with a recently proposed disturbed exchange model, suggesting that the result represents the first direct observation of the existence of antiferromagnetically coupled moments within an amorphous ferromagnetic alloy.