  The first amplitude analysis of the decay $D_s^+\to K^-K^+\pi^+\pi^0$ is
presented using the data samples, corresponding to an integrated luminosity of
6.32 fb$^{-1}$, collected with the BESIII detector at $e^+e^-$ center-of-mass
energies between 4.178 and 4.226 GeV. More than 3000 events selected with a
purity of 97.5\% are used to perform the amplitude analysis, and nine
components are found necessary to describe the data. Relative fractions and
phases of the intermediate decays are determined. With the detection efficiency
estimated by the results of the amplitude analysis, the branching fraction of
$D_s^+\to K^-K^+\pi^+\pi^0$ decay is measured to be $(5.42\pm0.10_{\rm
stat.}\pm0.17_{\rm syst.})\%$.
