In the previous work, we proposed the cluster-based composition analysis method for binary and ternary bulk metallic glasses, but found that the metallic glasses of complex systems do not satisfy single structural units. Taking the bulk metallic glass Zr55Cu30Al10Ni5 as a typical example, we extend the cluster-plus-glue-atom model to the dual-cluster case, that is, this alloy is regarded as a combination of Zr-Cu and Zr-Ni sub-system metallic glasses, with Al as the replacement atoms. The two clusters are derived from sub-systems, and all the possible combinations of glue atoms are calculated, combined with the 24-electron rule for ideal metallic glasses. Finally, the optimal dual-cluster formula of this quaternary alloy was determined theoretically, with higher glass forming ability exhibiting experimentally, indicating that this is the composition origin of the bulk metallic glass Zr55Cu30Al10Ni5 and the composition optimization is achieved. This work provides a quantifiable composition design method for multi-element metallic glasses.