Studies of yeast DNA topoisomerase II with various alanine-substitution mutations provide strong biochemical support of a recent hypothesis that the type IA and IIA DNA topoisomerases act similarly in their cleavage and rejoining of DNA. DNA breakage and rejoining by either a type IA or a type IIA enzyme are shown to involve cooperation between a DNA-binding domain containing the active-site tyrosine and a Rossmann fold containing several highly conserved acidic residues. For a homodimeric type IIA enzyme, cooperation occurs in trans: the active-site tyrosine in the DNA-binding domain of one protomer cooperates with several residues in the Rossmann fold as well as other regions of the other protomer.