Although amorphous materials lack long-range translation order, they are strongly ordered at the length scale of single interatomic bonds and retain some order into more distant coordination shells. One form of order is local, approximate rotational symmetry. For example, local five-fold rotational symmetry has been shown in simulations to correlate to slower dynamics in metallic liquids and greater strength in metallic glasses [1]. Local structural symmetry gives rise to symmetry in electron nanodiffraction speckle patterns acquired with sub-nanometer probes but evaluating symmetries in patterns from amorphous materials is challenging. Only small clusters of atoms have symmetry, their symmetry is often distorted or imperfect, and the symmetric cluster is embedded in more atoms which are disordered. One method to assess symmetries in nanodiffraction is the angular power spectrum. We have used angular power spectrum data to demonstrate that Zr65Cu27.5Al7.5 glasses exhibit increasing 4-fold and 5-fold structural symmetry with increasing stability in the glassy state and increasing hardness [2].