The fluorescence intensity of a single-stranded oligonucleotide containing a fluorene-labeled deoxyuridine $(U^{Fl})$ unit increases by only 1.5-fold upon formation of its perfectly matched duplex. To increase the fluorescence signal during hybridization, we positioned a quencher strand containing a deoxyguanine (dG) nucleobase, functioning as an internal quencher, opposite to the $U^{Fl}$ unit to reduce the intrinsic fluorescence upon hybridization with a probe. From an investigation of the optimal length of the quencher strand and the effect of the neighboring base sequence, we found that a short strand (five-nucleotide) containing all natural nucleotides and dG as an internal quencher was effective at reducing the intrinsic fluorescence of a linear beacon; it also exhibited high total discrimination factors for the formation of perfectly matched and single base-mismatched duplexes. Such assays that function based on clear changes in fluorescence in response to single-base nucleotide mutations would be useful tools for accelerating diagnoses related to various diseases.