The Sleeping Beauty transposon system, consisting of the transposon DNA and the transposase enzyme, is a member of the Tc1/mariner family of DNA transposons. Although it is an important tool in genetic applications and has been adapted for human gene therapy, its molecular mechanism remains obscure. Here, we use an experimental biophysics approach to study the molecular mechanism of the Sleeping Beauty transposon. We investigate the folding of the specific DNA recognition subdomain of the Sleeping Beauty transposase, the PAI subdomain. We show that only the folded PAI binds to DNA, however the amount of unfolded conformation is significant at close to physiologic conditions. We identify amino acid substitutions that result in stabilization of its folded conformation. Overall, our results provide a mechanistic insight into DNA recognition by the Sleeping Beauty transposase and suggest modifications to improve its activity.