Metallic glasses with pronounced high-frequency β relaxation in their dynamic-mechanical response have been observed to exhibit large plasticity. Due to their disordered atomic structure, it is challenging to identify the microscopic mechanisms of their relaxation behavior. Quasistatic anelastic relaxation measurements have been performed over 10 orders of magnitude of time on La_{55}Ni_{20}Al_{25} metallic glass, which exhibits a strong β relaxation. The corresponding time-constant spectra were computed from the data-they contain a series of peaks corresponding to an atomically quantized hierarchy of shear transformation zones (STZs), where both the α and β relaxations are consistent with the STZ model. Two different regimes of activation-volume increment between the peaks are observed, suggesting the involvement of different elements in STZs corresponding to α vs β relaxations. Room-temperature structural relaxation significantly affects the former but not the latter.