A statistically stationary and nearly homogeneous turbulent shear flow is established by an additional volume forcing in combination with stress-free boundary conditions in the shear direction. Both turbulent energy and enstrophy are stationary to a much better approximation than in previous simulations that use remeshing. The temporal fluctuations decrease with increasing Reynolds number. Energy spectra and shear-stress cospectra show that local isotropy is satisfactorily obeyed at the level of second-order moments. However, derivative moments of high order up to n = 7 yield increasing moments for n [ges ] 4 for the spanwise vorticity and the transverse derivative of the streamwise velocity in the range of Taylor Reynolds numbers 59 [les ] Rλ [les ] 99. These findings, which are in apparent violation of local isotropy, agree with recent measurements.