In this method, two oligonucleotide primers are hybridized to the same strand of a denatured double-stranded recombinant plasmid. One primer (the mutagenic primer) introduces the desired mutation into the target sequences, whereas the second primer carries a mutation that destroys a unique restriction site (called “unique site elimination,” or USE) in the plasmid. The product of the first part of the method is a heteroduplex plasmid consisting of a wild-type parental strand and a new full-length strand that carries the desired mutation but no longer contains the unique restriction site. In the second phase of the method, the mixed population is incubated with the restriction enzyme that cleaves the unique site. The wild-type molecules are linearized, and the mutated plasmids are resistant to digestion. The mixture of circular heteroduplex DNA and linear wild-type DNA is then used to transform a strain of Escherichia coli that is deficient in repair of mismatched bases. The circular heteroduplex molecules begin to replicate while many of the linear wild-type molecules are unable to reestablish themselves in E. coli cells. Because the mismatched bases are not repaired, the first round of replication generates a wild-type plasmid that carries the original restriction site and a mutated plasmid that does not. DNA from the first set of transformants is recovered, digested once more with the same restriction enzyme to linearize the wild-type molecules, and then used to transform a standard laboratory strain of E. coli.