This disclosure provides, among other things, a method of combining nucleic acid fragments, comprising: (a) providing two double-stranded DNA molecules with a common sequence, wherein the common sequence is at the end of each molecule; (b) nicking one strand in the common sequence of both molecules at a respective nicked site; (c) moderately denaturing both molecules to remove a single-stranded fragment from the nicked site to one end of each molecule, wherein the single-stranded fragment includes the common sequence in part or in whole, resulting in an overhanging sequence in each molecule, and the overhanging sequences in both molecules are complementary to each other; (d) allowing the overhanging sequences of both molecules to anneal to each other, and ligating the molecules. Alternative ways for performing the method are also provided.