Current neutrino oscillation data indicate that θ13 is not strongly suppressed and θ23 might have an appreciable deviation from π/4, implying that the 3×3 neutrino mixing matrix V does not have an exact μ–τ permutation symmetry. We make a further study of the effect of μ–τ symmetry breaking on the democratic flavor distribution of ultrahigh-energy (UHE) cosmic neutrinos at a neutrino telescope, and find that it is characterized by |Vμi|2−|Vτi|2 which would vanish if either θ23=π/4 and θ13=0 or θ23=π/4 and δ=±π/2 held. We observe that the second-order μ–τ symmetry breaking term Δ¯ may be numerically comparable with or even larger than the first-order term Δ in the flux ratios ϕeT:ϕμT:ϕτT≃(1−2Δ):(1+Δ+Δ¯):(1+Δ−Δ¯), if sin(θ23−π/4) and cosδ have the same sign. The detection of the UHE ν¯e flux via the Glashow-resonance channel ν¯ee→W−→anything is also discussed by taking account of the first- and second-order μ–τ symmetry breaking effects.