A partial-wave analysis of the decay $J/psi to K^+K^-pi^0$ has been made using $(223.7pm1.4)times 10^{6}$ $J/psi$ events collected with the BESIII detector in 2009. The analysis, which is performed within the isobar-model approach, reveals contributions from $K^*_2(1430)^pm$, $K^*_2(1980)^pm$ and $K^*_4(2045)^pm$ decaying to $K^pmpi^0$. The two latter states are observed in $J/psi$ decays for the first time. Two resonance signals decaying to $K^+K^-$ are also observed. These contributions can not be reliably identified and their possible interpretations are discussed. The measured branching fraction $B(J/psi to K^+K^-pi^0)$ of $(2.88pm0.01pm0.12)times10^{-3}$ is more precise than previous results. Branching fractions for the reported contributions are presented as well. The results of the partial-wave analysis differ significantly from those previously obtained by BESII and BABAR.
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