This paper presents a new optimal second-order design of the infinite impulse response digital differentiator. This design manifests the L1-error fitness function’s optimization using the multi-verse optimization algorithm. The optimizing variables are obtained from the direct wave-form-based transfer function. The acquired magnitude response approximates the ideal differentiator with the mean absolute magnitude error −45.8842 dB. The designed optimal differentiator has also been compared with the existing designs to manifests its efficacy.