We present evidence for the presence of complex anisotropy in the lowermost mantle from 3-D waveform modelling of observed core-diffracted shear waves that sample the southern edge of the African Large Low Shear Velocity Province (LLSVP). The anomalously strong amplitude of the SV component for the shear core-diffracted phase at large distances indicates the presence of anisotropy. We measure shear wave splitting parameters to determine which part of the elastic tensor is constrained by this particular data set. The modelling is performed using the spectral element method. The anisotropy is strong outside the LLSVP, weakens or rotates close to its boundary, and appears to be absent inside the LLSVP. The presence of the LLSVP margin may cause flow in the mantle to change direction. The occurrence of strong anisotropy in the region of fast seismic velocities is compatible with lattice-preferred orientation in post-perovskite due to accommodation of flow through dislocation creep.