The p53 tumor suppressor protein is a tetramer that binds sequence-specifically to a DNA consensus sequence consisting of two consecutive half-sites, with each half-site being formed by two head-to-head quarter-sites (--><-- --><--). Each p53 subunit binds to one quarter-site, resulting in all four DNA quarter-sites being occupied by one p53 tetramer. The tetramerization domain forms a symmetric dimer of dimers, and two contrasting models have the two DNA-binding domains of each dimer bound to either consecutive or alternating quarter-sites. We show here that the two monomers within a dimer bind to a half-site (two consecutive quarter-sites), but not to separated (alternating) quarter-sites. Tetramers bind similarly, with the two dimers within each tetramer binding to pairs of half-sites. Although one dimer within the tetramer is sufficient for binding to one half-site in DNA, concurrent interaction of the second dimer with a second half-site in DNA drastically enhances binding affinity (at least 50-fold). This cooperative dimer-dimer interaction occurs independently of tetramerization and is a primary mechanism responsible for the stabilization of p53 DNA binding. Based on these findings, we present a model of p53 binding to the consensus sequence, with the tetramer binding DNA as a pair of clamps.