In order to improve the fatigue strength of Zr₅₀Cu₄₀Al₁₀ BGAs during 10³–10⁴ cycles, we tried to use the small additive element. As a result, Pd, Ag, Pt, and Au are effective addition elements to enhance the fatigue strength. Especially, the additive Pd element has a beneficial effect on the fatigue-strength enhancement. The additive Pd element promotes the glass-structure expansion, which can be recognized from the volume change due to the structural relaxation. Consequently, we found the linear relationship between the fatigue limit and volume change in Zr₅₀Cu_40−XAl₁₀Pd_X [X: 0–7 atomic percent (at%)] glassy alloys. Furthermore, we conclude that the origin of the unique hardness distribution on the fatigue-fractured surface is probably related to hydrogen hardening. The Zr₅₀Cu₃₇Al₁₀Pd₃ glassy alloy, which exhibits the highest fatigue limit of 1,050 MPa, shows a superior resistance force against the hydrogen hardening. Thus, maintaining the balance between the hardening and embrittlement around the fatigue crack tip by hydrogen is the significant factor to enhance the fatigue strengths.