—Redundancy Addition and Removal (RAR) is a restructuring technique used in the synthesis and optimization of logic designs. It can remove an existing target wire and add an alternative wire in the circuit such that the functionality of the circuit is intact. However, not every irredundant target wire can be successfully removed due to some limitations. Thus, this paper proposes a new restructuring technique, IRredundancy Removal and Addition (IRRA), which successfully removes any desired target wire by constructing a rectification network which exactly corrects the error caused by removing the target wire.