The creation of large phage antibody libraries has become an important goal in selecting antibodies against any antigen. Here we describe a method for making libraries so large that the complete diversity cannot be accessed using traditional phage technology. This involves the creation of a primary phage scFv library in a phagemid vector containing two nonhomologous lox sites. Contrary to the current dogma, we found that infecting Cre recombinase-expressing bacteria by such a primary library at a high multiplicity of infection results in the entry of many different phagemid into the cell. Exchange of Vh and Vl genes between such phagemids creates many new V h/Vl combinations, all of which are functional. On the basis of the observed recombination, the library is calculated to have a diversity of 3x1011. A library created using this method was validated by the selection of high affinity antibodies against a large number of different protein antigens.