Cooperativity is a central feature of protein folding, but the thermodynamic and structural origins of cooperativity remain poorly understood. To quantify cooperativity, we measured guanidine-induced unfolding transitions of single helix-hairpin-helix (HhH)2 repeats and tandem pairs from a seven-repeat segment of Methanopyrus kandleri Topoisomerase V (Topo V) to determine intrinsic repeat stability and interfacial free energies between repeats. Most single-repeat constructs are folded and stable; moreover, several pairs have unfolding midpoints that exceed midpoints of the single repeats they comprise, demonstrating favorable coupling between repeats. Analyzing unfolding transitions with a modified Ising model, we find a broad range of intrinsic and interfacial free energies. Surprisingly, the G repeat, which lacks density in the crystal structure of Topo V without DNA, is the most stable repeat in the array. Using nuclear magnetic resonance spectroscopy, we demonstrate that the isolated G repeat adopts a canonical (HhH)2 fold and forms an ordered interface with the F-repeat but not with the H repeat. Using parameters from our paired Ising fit, we built a partition function for the seven-repeat array. The multistate unfolding transition predicted from this partition function is in excellent agreement with the experimental unfolding transition, providing strong justification for the nearest-neighbor model. The seven-repeat partition function predicts a native state in which three independent segments ("stability islands") of interacting repeats are separated by two unstable interfaces. We confirm this segmented architecture by measuring the unfolding transition of an equimolar mixture of these three separate polypeptides. This segmented structural organization may facilitate wrapping around DNA.