Fast vertical flapping oscillations of the plasma sheet have been observed by Cluster on September 26, 2001. The flapping motion had vertical speeds exceeding 100 km/s, an amplitude in excess of 1 RE and a quasiperiod of ~3 min. The current sheet was mostly tilted in the Y-Z plane (with the tilt sometimes exceeding 45°). The waves had the properties of a kink mode and propagated toward the dusk flank. The flapping allowed to probe the vertical structure of the plasma sheet. Three different methods gave consistent evidence of a bifurcated structure of the cross-tail current with about half of all current concentrated in two sheets (each ~500-1000 km thick). The current density peaks at |Bx| ~ 0.5 BL, with a pronounced current density minimum and a plasma density plateau between these peaks.