A month of digital data from two three component seismograph stations near Wellington, New Zealand, was analysed as part of a feasibility study for a major project to investigate shear‐wave splitting. Although the total number of earthquakes studied was small (14), some suggestive results were obtained. Almost all events recorded within the shear wave window showed a phase reversal of the horizontal components after one or two shear wave cycles, suggesting that there are actually two shear‐wave arrivals. The measured polarization of the first shear wave arrivals was N (31 +/−11) E. This polarization alignment cannot be explained by focal mechanisms, and it is unlikely to be due to topography because of the station‐to‐station correlation. The present evidence suggests the most likely cause is crustal anisotropy due to the geological structure at shallow depth, rather than stress aligned micro‐cracks. Copyright 1990 by the American Geophysical Union.