Abstract: A method of cloning DNA fragments is disclosed comprising the steps of: (a) cleaving a vector DNA of plasmid origin with a restriction enzyme, (b) dephosphorylating an end of the cleaved DNA, (c) separately obtaining a mixture of DNA fragments by cleaving a chromosomal DNA with a restriction enzyme creating ends cohesive to those crated in step (a) in the vector DNA, (d) obtaining a mixture of ligated DNAs through ligation using the dephosphorylated DNAs of step (b) and the mixture of DNA fragments of step (c), (e) amplifying the ligated DNAs by PCR with a vector-specific arbitrary primer for the vector employed in step (a) and one or more non-vector-specific arbitrary primers, using the mixture of ligated DNAs as templates, and at an annealing temperature of not lower than 55° C., and (f) introducing into a competent cell a cloning vector into which is incorporated a PCR product thus obtained.