Shear‐wave splitting measurements are made using teleseismic S, ScS and SKS waveforms recorded at the GDSN broadband station SNZO, situated in South Karori, New Zealand. The average S and SKS delay times are around 2 to 3 s, among the highest in the world. The average ScS delay time is significantly smaller, around 1 s. This discrepancy appears to be due to differences in dominant frequency. The most likely cause of frequency‐dependent anisotropy is oriented heterogeneities with a scale‐length much smaller than the wavelength. The fast polarizations range between 21° and 79°, with an average NE‐SW direction which is sub‐parallel to the trend of the local geologic structure and the strike of the Hikurangi subduction zone. Azimuthal variations in delay time, which cannot be explained by differences in period, may be due to a dipping axis of symmetry, or laterally varying anisotropy, or a more complicated symmetry system.