We observe density-induced 90 degrees rotations of the anisotropy axes in transport measurements at half-filled high Landau levels in the two dimensional electron system, where stripe states are proposed ( nu = 9/2, 11/2, etc.). Using a field effect transistor, we find the transition density to be 2.9x10(11) cm(-2) at nu = 9/2. Hysteresis is observed in the vicinity of the transition. We construct a phase boundary in the filling factor magnetic field plane in the regime 4.4<nu<4.6. An in-plane magnetic field applied along either anisotropy axis always stabilizes the low density orientation of the stripes.