Eukaryotic DNA-binding protein replication protein A (RPA) has a strand melting property that assists polymerases and helicases in resolving DNA secondary structures. Curiously, previous results suggested that human RPA (hRPA) promotes undesirable recombination by facilitating annealing of flaps produced transiently during DNA replication; however, the mechanism was not understood. We designed a series of substrates, representing displaced DNA flaps generated during maturation of Okazaki fragments, to investigate the strand annealing properties of RPA. Until cleaved by FEN1 (flap endonuclease 1), such flaps can initiate homologous recombination. hRPA inhibited annealing of strands lacking secondary structure but promoted annealing of structured strands. Apparently, both processes primarily derive from the strand melting properties of hRPA. These properties slowed the spontaneous annealing of unstructured single strands, which occurred efficiently without hRPA. However, structured strands without hRPA displayed very slow spontaneous annealing because of stable intramolecular hydrogen bonding. hRPA appeared to transiently melt the single strands so that they could bind to form double strands. In this way, melting ironically promoted annealing. Time course measurements in the presence of hRPA suggest that structured single strands achieve an equilibrium with double strands, a consequence of RPA driving both annealing and melting. Promotion of annealing reached a maximum at a specific hRPA concentration, presumably when all structured single-stranded DNA was melted. Results suggest that displaced flaps with secondary structure formed during Okazaki fragment maturation can be melted by hRPA and subsequently annealed to a complementary ectopic DNA site, forming recombination intermediates that can lead to genomic instability.