During the last decade, the presence of velocity anisotropy inside the inner core, with a fast axis parallel to the Earth's rotation axis, has been well established. The quantitative analysis of the amplitudes of waves which sample a particular region of the inner core, under Africa, but exhibit various orientations allows us to document and characterize the presence of anisotropy in attenuation. The analysis is based on a comparison of both amplitudes and travel times of the PKP(DF) wave, which samples the inner core, and the PKP(BC) wave, which has nearly the same path but bottoms inside the liquid core. The data reveal that the direction of strong attenuation correlates with that of fast velocity. When referred to the same epicentral distance and focal depth, the PKP(DF)/PKP(BC) amplitude ratio are about five times lower for paths tilted by 25¿ with respect to the Earth rotation axis, than for nearly equatorial paths. A clear negative correlation is observed between travel time and amplitude residuals, when the angle to Earth rotation axis varies. This first quantitative analysis, combined with experimental results on oriented crystals and mushy media, may bring important constraints on the mechanism responsible for anisotropy in the inner core. ¿ American Geophysical Union 1996