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The location of the plasma sheath edge, where quasineutrality is broken, is rigorously derived by using a kinetic description of the plasma. It is shown that sheaths can exist with arbitrarily small ion velocity at the sheath edge, thus violating the Bohm criterion, Vi = cs at the sheath edge. Bohm’s criterion is recovered in the case of large enough ion current through the wall, and it is found to be a reasonable approximation in floating potential conditions. However, in the case of a predominant electron current through the wall, Bohm’s criterion is not able to describe the sheath-edge transition. The analytical results are supported by numerical simulations performed with a fully kinetic particle-in-cell code modeling a source-driven, weakly collisional plasma, bound between two absorbing walls.