Peptidyl arms extending from one protein domain to another protein domain mediate many important interactions in biology. A well-studied example of this type of protein-protein interaction occurs between the yeast homeodomain proteins, MAT alpha2 and MAT a1, which form a high-affinity heterodimer on DNA. The carboxyl-terminal arm extending from MAT alpha2 to MAT a1 has been proposed to produce an allosteric conformational change in the a1 protein that generates a very large increase in the DNA binding affinity of a1. Although early studies lent some support to this model, a more recent crystal structure determination of the free a1 protein argues against any allosteric change. This note presents a thermodynamic argument that accounts for the proteins' binding behavior, so that allosteric conformational changes are not required to explain the large affinity increase. The analysis presented here should be useful in analyzing binding behavior in other systems involving arm interactions.