  A partial-wave analysis of the decay $J/\psi \to K^+K^-\pi^0$ has been made
using $(223.7\pm1.4)\times 10^{6}$ $J/\psi$ 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 $K^\pm\pi^0$. 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 $(2.88\pm0.01\pm0.12)\times10^{-3}$ 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.
