The Holliday junction is a key intermediate in genetic recombination. It consists of four strands of DNA that associate to form four double-helical arms. Studies over the past decade with asymmetric analogs of Holliday junctions have shown that the four arms stack to generate two stacking domains. This arrangement of arms results in two strands with a roughly helical structure, and two that contain a crossover structure connecting the domains. Both parallel and antiparallel orientations of the helical strands are possible, although the antiparallel orientation is favored. In principle, there are two possible isomers of the Holliday junction, depending on which pairs of strands contain the crossover structure; isomerization between these two structures is key to many molecular models of recombination. Isomerization of parallel domain structures entails large end-to-end helical rotations if braiding of the crossover strands is to be avoided. We have examined the ability of the crossover strands to braid. This has been done by employing a double crossover molecule, whose termini are all hairpin loops. Such a molecule is a catenane of two single strands of DNA, whose linking number is a function of the sign of the node at the crossover. We have prepared linking standards by means of topological protection techniques, and have compared them to the catenane formed by the double crossover molecule. We find no evidence for braiding of the strands. Furthermore, no braided structures can be detected when the double crossover molecule is treated with Escherichia coli DNA topoisomerase I in the presence of varying amounts of Mg2+ cations.