Flap endonucleases (FENs) isolated from archaea are shown to recognize and cleave a structure formed when two overlapping oligonucleotides hybridize to a target DNA strand. The downstream oligonucleotide probe is cleaved, and the precise site of cleavage is dependent on the amount of overlap with the upstream oligonucleotide. We have demonstrated that use of thermostable archaeal FENs allows the reaction to be performed at temperatures that promote probe turnover without the need for temperature cycling. The resulting amplification of the cleavage signal enables the detection of specific DNA targets at sub-attomole levels within complex mixtures. Moreover, we provide evidence that this cleavage is sufficiently specific to enable discrimination of single-base differences and can differentiate homozygotes from heterozygotes in single-copy genes in genomic DNA.