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) (${Phi}8$ mm). The possible mechanisms underlying the enhancement of the glass forming ability by this alloy are discussed based on the dimensionless parameter ${gamma}$. In addition, alloy design strategy for the improvement of GFA is proposed in the viewpoint of heat of mixing (${Delta}H_{mix}$)difference and atomic packing state.