Given its importance in parametrizing eddies, we consider the orientation of eddy flux of potential vorticity (PV) in geostrophic turbulence. We take two different points of view, a classical ensemble- or time-average point of view and a second scale decomposition point of view. A net alignment of the eddy flux of PV with the appropriate mean gradient or the large-scale gradient of PV is required. However, we find this alignment to be very weak. A key finding of our study is that in the scale decomposition approach, there is a strong correlation between the eddy flux and a nonlinear combination of resolved gradients. This strong correlation is absent in the classical decomposition. This finding points to a new model to parametrize the effects of eddies in global ocean circulation.