a tagged amplifiable library vh phage with an untagged library free vl chains pick the best vh express the vh as free chains and use these free chains to select the best vl chains from a vl phage library the total complexity screened can be as high as the product the two library sizes approximately 10 8 u00d7 10 8 10 16 a primary goal of random peptide library generating and screening methods is to increase the effective size of the library theoretically one should be able to obtain more and higher affinity ligands with larger libraries phage and other random peptide libraries typically consist of 10 12 total particles with 10 9 different binding sites the effective number of different binding sites can be increased by combinatorial association with a library of synthetic peptides high affinity peptide protein association is provided by the dimerization of two copies of an association peptide of the invention one copy of which is present in the random peptide containing library fusion protein and one copy of which is present in each member of a collection of random synthetic peptides in a phage based random peptide library in which the random peptide is displayed as a fusion with a coat protein such as the piii or pviii coat proteins one can assume there are five copies of the piii fusion protein per phage the present method produces for a library of 10 9 different phage 10 12 total copies and upon the addition of 5 u00d7 10 9 different peptides.