The turbulence in plane Couette flow subjected to system rotation is investigated. The anti-cyclonic rotation rate is well above the range in which roll-cells occur and close to the upper bound, beyond which no stationary turbulent states of motion exist. The mean velocity profile exhibits a linear region over 80% of the cross-section, in which the mean absolute vorticity is driven to zero. Viscous effects still prevail in narrow regions next to the walls, whereas the quasi-homogeneous central core exhibits abnormal anisotropies of the Reynolds stress tensor, the vorticity tensor and the energy dissipation rate tensor. In spite of the distinctly higher turbulence level observed, a 13% drag reduction is found. This paradoxical finding is ascribed to configurational changes in the turbulence field brought about by the system rotation.