A pronounced secondary β-relaxation is observed in a newly-developed La-based bulk metallic glass that has critical size at least 10mm in diameter. It is demonstrated that the β-relaxation becomes pronounced with increasing annealing time due to decoupling from the α relaxation. By using nanoindentation, we find that the shear-transformation-zone (STZ) volume and involved atoms increase in the annealed samples, implying that the decoupling of the β-relaxation from the α relaxation can promote the movement of local atoms. However, the correlation of β-relaxation with ambient compressive plasticity of bulk samples is not revealed.