We prove the equivalence between the category RigDM eff ét (K, Q) of effective motives of rigid analytic varieties over a perfect complete non-archimedean field K and the category RigDA eff Frobét (K, Q) which is obtained by localizing the category of motives without transfers RigDA eff ét (K, Q) over purely inseparable maps. In particular, we obtain an equivalence between RigDM eff ét (K, Q) and RigDA eff ét (K, Q) in the characteristic 0 case and an equivalence between DM eff ét (K, Q) and DA eff Frobét (K, Q) of motives of algebraic varieties over a perfect field K. We also show a relative and a stable version of the main statement.