Previously, we reported on the discovery of fine structure in whistler data received on the ground at Halley, Antarctica. This structure was not apparent in conventional spectral analysis but was revealed by the technique of digital matched filtering. We have now examined a larger data set, and a commonly observed phenomenon is that single whistler traces become split into two, over various frequency ranges. Examples are presented in the form of time-transformed spectrograms in which reference model whistlers are represented as vertical lines. The splitting is typically 5–15 ms (about 0.5% of the total whistler travel time) and extends over frequency ranges of a few hundred hertz which may occur anywhere between the upper and lower cutoff frequencies of the whistler. The splitting may be either symmetrical or unsymmetrical with respect to the unsplit trace. The effect is unlikely to arise in the spectrum of the lightning source or from propagation under or through the ionosphere. It may, however, be a signature of field-aligned fine spatial structure in plasmaspheric density, and hence refractive index, in the whistler duct. For simple longitudinal propagation, electron density fluctuations of the order of 1% and spatial scale sizes of the order of 50 km in the equatorial plane are implied. It seems possible that the observations could also be interpreted in terms of the mode theory of ducted propagation, assuming the excitation of two modes with group velocities differing by a few tenths of a percent.