Traditionally, recombination reactions promoted by RecA-like proteins initiate by forming a nucleoprotein filament on a single-stranded DNA (ssDNA), which then pairs with homologous double-stranded DNA (dsDNA). In this paper, we describe a novel pairing process that occurs in an unconventional manner: RecA protein polymerizes along dsDNA to form an active nucleoprotein filament that can pair and exchange strands with homologous ssDNA. Our results demonstrate that this "inverse" reaction is a unique, highly efficient DNA strand exchange reaction that is not due to redistribution of RecA protein from dsDNA to the homologous ssDNA partner. Finally, we demonstrate that the RecA protein-dsDNA filament can also pair and promote strand exchange with ssRNA. This inverse RNA strand exchange reaction is likely responsible for R-loop formation that is required for recombination-dependent DNA replication.