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Using (2.712±0.014)×109 ψ(2S) events collected with the BESIII detector operating at the BEPCII, we search for the ηc(2S)→K+K-η′ decay. Its decay branching fraction is measured to be (11.11±4.67(stat)±1.82(syst)±4.24(extr))×10-4, where the first uncertainty is statistical, the second is systematic, and the third uncertainty is from the branching fraction of the ψ(2S)→γηc(2S) decay. The statistical significance is 2.8σ. The upper limit on the product branching fraction B[ψ(2S)→γηc(2S)]×B[ηc(2S)→K+K-η′] is set to be 0.94×10-6 at 90% confidence level. In addition, the branching fractions of χc1→K+K-η′ and χc2→K+K-η′ are updated to be (8.48±0.10(stat)±0.47(syst))×10-4 and (1.53±0.04(stat)±0.08(syst))×10-4, respectively. The precision is improved by twofold.