IS607-family transposons are unusual because they do not have terminal inverted repeats or generate target site duplications. They encode two protein-coding genes, but only tnpA is required for transposition. Our X-ray structures confirm that TnpA is a member of the serine recombinase (SR) family, but the chemically-inactive quaternary structure of the dimer, along with the N-terminal location of the DNA binding domain, are different from other SRs. TnpA dimers from IS1535 cooperatively associate with multiple subterminal repeats, which together with additional nonspecific binding, form a nucleoprotein filament on one transposon end that efficiently captures a second unbound end to generate the paired-end complex (PEC). Formation of the PEC does not require a change in the dimeric structure of the catalytic domain, but remodeling of the C-terminal α-helical region is involved. We posit that the PEC recruits a chemically-active conformer of TnpA to the transposon end to initiate DNA chemistry.