In general, fiber orientation distribution functions are defined as symmetric spherical functions. The present work shows how local averaging can be used to compute averaged asymmetric fODF (ava-fODF) from input symmetric white matter (WM) fODF. The resulting ava-fODF shows the presence of asymmetric patterns in voxels containing multiple crossings as well as along the white matter/gray matter interface. Moreover, the proportion of WM voxels displaying asymmetric features after filtering accounts for at least 30% of all WM voxels. Ava-fODF reveals new possibilities for classification of fiber configurations, with unidirectional fODF, bending fODF, Y-branching fODF and other complex fiber configurations.