A new Cu-Hf-Al-Be monolithic bulk amorphous alloy was developed utilizing minimal use of toxic and expensive Be. The developed alloy exhibits a large glass forming ability (GFA) (Φ8 mm). The possible mechanisms underlying the enhancement of the glass forming ability by this alloy are discussed based on the dimensionless parameter γ. In addition, alloy design strategy for the improvement of GFA is proposed in the viewpoint of heat of mixing (ΔH(mix))difference and atomic packing state.