The present invention provides a novel method for nucleic acid amplification. The method includes contacting the sample with at least one forward primer and at least one reverse primer, an AP endonuclease, and a nucleic acid polymerase. under conditions sufficient to allow the forward and reverse primers to hybridize to the target nucleic acid and form a reaction mixture, wherein at least one of the forward and reverse primer includes an AP endonuclease-cleavable linker L, and incubating the reaction mixture under reaction conditions that simultaneously allow the AP endonuclease to cleave at a linker site L and the extension of the primers in a template-specific manner to amplify the target nucleic acid sequence.