The determination of structure from the inversion of teleseismic receiver functions may be improved by removing the contribution of the free surface. The free surface interaction gives rise to the highest amplitude signal on standard receiver functions and yet this initial pulse tells us little about the receiver structure below the surface layer. We apply a transformation to P, S and Horizontal wavevector components, which removes the free surface response and hence the initial P-pulse. A pure receiver function is calculated by deconvolving the S-wavevector component with the P-wavevector. In general, converted phase amplitudes within the receiver function waveform are better matched by the inverse algorithm, resulting in an improved estimation of seismic structure. In particular, low amplitude receiver function waveforms, often associated with poorly constrained structure, now yield a successful inverse.