Disclosed are methods for detecting a target nucleic acid in a sample. The methods include contacting the sample, in the presence of a polymerase and an endonuclease, with a first oligonucleotide comprising, in the 5′ to 3′ direction, a first signal DNA generation sequence, an endonuclease recognition site, and a sequence complementary to the 3′ end of a target nucleic acid; a second oligonucleotide comprising, in the 5′ to 3′ direction, a second signal DNA generation sequence, an endonuclease recognition site, and a sequence that is homologous to the first signal DNA generation sequence of the first oligonucleotide; a third oligonucleotide comprising, in the 5′ to 3′ direction, a third signal DNA generation sequence, an endonuclease recognition site, and a sequence that is homologous to the second signal DNA generation sequence of the second oligonucleotide.