Federated　learning　allows　multiple　clients　to　train　a　global　model　without　data　exchanging.　But　in　real　world,　the　global　model　is　not　suitable　for　all　clients　because　they　may　hold　heterogenous　data　and　have　personalized　and　individual　demands,　which　will　directly　weaken　the　motivation　of　them　to　participate　in　federated　learning.　To　make　each　client　benefits　from　federated　learning,　researchers　propose　to　train　personalized　models　from　global　model　using　local　data.　However,　the　lack　of　raw　data　in　the　model　retraining　process　will　lead　to　the　challenge　of　forgetting,　which　can　deprive　the　personalized　model　of　the　benefits　gained　from　federated　learning.　In　extreme　cases　(e.g.,　the　client　lacks　certain　classes　of　data),　the　ability　to　recognize　the　lacked　data　may　even　be　completely　forgotten.　To　this　end,　we　propose　a　local　adaptation　method　to　overcome　forgetting,　which　add　the　generator　synthetic　data　to　local　adaptation　to　realize　model　updating　incrementally.　We　test　our　method　on　real-world　datasets,　and　the　results　show　that　when　adopting　the　proposed　method　on　local　adaptation,　the　clients　can　get　flexible　adaption　ability　to　new　data　as　well　as　keep　the　original　recognition　capability　of　the　global　model　even　in　extreme　cases.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG.