Time–frequency　analysis　(TFA)　can　effectively　characterize　features　of　non-stationary　signals.　Traditional　TFA　algorithms　construct　signal　models　in　the　time　domain　and　make　the　assumption　that　the　instantaneous　characteristics　of　each　component　are　continuous.　However,　the　instantaneous　frequency　(IF)　of　the　transient　signal　is　discontinuous　in　the　time　domain　and　exhibits　a　multifaceted　relationship　with　time,　such　as　shock,　vibration　wave,　damped　sound　wave,　etc.　Additionally,　in　most　existing　TFA　methods,　low-order　group　delay　(GD)　is　used　to　describe　transient　signals,　which　leads　to　unsatisfactory　energy　concentration　and　calculation　accuracy.　To　address　about　issues,　a　novel　TFA　technique,　termed　high-order　iterative　rearrangement　transform　(HOIRT),　is　developed　in　this　research.　First,　the　signal　model　is　defined　within　the　frequency　domain,　and　the　frequency　ridge　of　the　transient　signal　is　described　by　a　high-order　GD　(HOGD),　which　is　similar　to　the　IF.　Second,　a　HOGD-based　iterative　synchrosqueezing　operator　is　defined　to　reassign　time–frequency　coefficients　into　the　GD　trajectories　along　the　time　direction.　Finally,　the　HOGD-based　frequency　extraction　operator　is　constructed　to　only　retain　the　target　time–frequency　information　of　the　transient　signal　from　the　rearranged　results,　such　that　the　noise　interference　is　eliminated　and　the　energy-concentrated　TFR　is　obtained.　A　simulation　signal　with　nonlinear　GDs　is　employed　to　illustrate　the　effectiveness　of　the　HOIRT.　Compared　with　the　other　seven　typical　TFA　algorithms,　the　developed　technique　has　the　smallest　calculation　error　and　Rényi　entropy,　showing　that　the　HOIRT　has　the　highest　accuracy　and　energy　concentration.　Analysis　result　of　the　bearing　fault　impact　signal　shows　that　the　proposed　HOIRT　can　display　the　time　when　pulses　occur　while　ensuring　high　time–frequency　resolution,　making　it　suitable　for　detecting　bearing　faults.　©　The　Author(s)　2024.