We　study　the　problem　of　maximizing　non-monotone　submodular　functions　subject　to　a　p-independence　system　constraint.　Although　the　submodularity　ratio　has　been　well-studied　in　maximizing　set　functions　under　monotonic　scenario,　the　defined　parameter　may　bring　hardness　of　approximation　for　the　maximization　of　set　functions　in　the　non-monotonic　case.　In　this　work,　utilizing　a　lower　bound　for　the　marginal　values,　we　investigate　the　Repeated　Greedy　introduced　by　(Feldman　et　al.　2017)　and　obtain　a　parameterized　performance　guarantee　for　the　above　constrained　submodular　maximization　problem.　©　2021,　Springer　Nature　Switzerland　AG.