Travel-time residuals of the PKIKP phase observed between 170¿ and 180¿ show an axisymmetric pattern of degree 2 with an amplitude of about 2 seconds. The effect at shorter distances is much less pronounced and the entire data set cannot be explained by a physically realistic radial distribution of (isotropic) heterogeneity. We propose that, in addition to the general (isotropic) heterogeneity, the inner core is anisotropic with cylindrical symmetry aligned with the earth's rotation axis. Average P-velocity along this axis is about 1 percent faster than the equatorial plane.