The　super-twisting　algorithm　(STA)-based　robust　exact　differentiator　(RED)　proposed　by　Levant　has　been　widely　applied　in　control,　observation,　and　fault　detection.　With　properly　set　parameters,　STA-RED　is　able　to　estimate　exactly　and　robustly　the　derivatives　of　an　input.　With　a　given　input　signal,　however,　a　practical　parameter　tuning　rule　still　lacks.　To　this　end,　a　general　parameter　tuning　algorithm　with　the　full　stability　proof　for　STA-RED　is　proposed.　In　particular,　the　time　linear　transformation　and　the　coordinate　transformation　are　performed　on　a　given　base　signal,　allowing　the　deterministic　relationship　between　the　parameters　of　STA-RED　and　the　amplitude　and　the　frequency　of　the　input　to　be　obtained.　The　full　stability　of　the　STA-RED　based　on　the　proposed　parameter　tunning　algorithm　(denoted　as　PSTA-RED)　with　perturbations　is　given　using　the　Lyapunov　function　method.　The　simulations　are　carried　out　using　given　input　signals　and　the　pressure　signals　from　the　altitude　ground　test　facility　to　illustrate　the　effectiveness　of　the　proposed　PSTA-RED.　©　The　Author(s)　2024.