In the framework of perturbative QCD, the radiative decays J/ψ→γη(′) are revisited in detail, where the involved one-loop integrals are evaluated analytically with the light quark masses kept. We have found that the sum of loop integrals is insensitive to the light quark masses and the branching ratios B(J/ψ→γη(′)) barely depend on the shapes of η(′) distribution amplitudes. With the parameters of η−η′ mixing extracted from low energy processes and J/ψ→γη(′) by means of nonperturbative matrix elements 〈0|GμνaG˜a,μν|η(′)〉 based on UA(1) anomaly dominance argument, we could not give the ratio RJ/ψ in agreement with experimental result. However, using the parameters, especially the mixing angle ϕ=33.5∘±0.9∘, extracted from γ⁎γ−η′ transition form factor measured at q2=112 GeV2 by BaBar collaboration, we obtain RJ/ψ=4.70 in good agreement with RJ/ψexp=4.65±0.21. As a crossing check, with Γexp(η(′)→γγ) and our results for J/ψ→γη(′), we get ϕ=33.9∘±0.6∘. The difference between the determinations of ϕ is briefly discussed.