A curious observation has been made on radial receiver functions calculated from teleseisms recorded by 29 broad-band seismometers distributed over Iceland. The arrival time of the direct P phase of the radial receiver functions depends critically upon the azimuth of the teleseismic source. For a seismic station in West Iceland, the direct P phase of the radial receiver function arrives consistently later for easterly source azimuths than for westerly source azimuths. The reverse applies for stations in East Iceland. In the original seismograms, the delayed P phase of the receiver function appears up to 450 ms later on the radial than on the vertical component. The seismometer locations in East and West Iceland are separated by the Neovolcanic Zone, a constructive plate boundary. The delayed P phases occur for seismic rays travelling across this zone. However, it is not obvious how wave propagation across the plate boundary zone could cause the observed delays. The tentative explanation proposed here involves the regional dip of the Icelandic lava sequences towards the Neovolcanic Zone. A dipping interface at shallow depth results in a P-S converted phase arriving shortly after the P phase. These phases cannot be separated in the radial receiver functions, given the bandwidth of the observed signals. However, a calculation of receiver functions from estimates of the P, SV and SH wavefields clearly reveals a P-S converted phase at about 500 ms for easterly source azimuths in West Iceland and for westerly source azimuths in East Iceland. The amplitudes of the direct P phase and the P-S phase converted at a dipping interface would be expected to vary strongly with azimuth in accordance with the observed behaviour.