We demonstrate a new method of x-ray absorption spectroscopy (XAS) that is bulk sensitive, like traditional fluorescence yield measurements, but is not affected by self-absorption or saturation effects. This measure of XAS is achieved by scanning the incident photon energy through an absorption edge and using an energy sensitive photon detector to measure the partial fluorescence yield (PFY). The x-ray emission from any element or core-hole excitation that is not resonant with the absorption edge under investigation is selected from the PFY. It is found that the inverse of this PFY spectrum, which we term inverse partial fluorescence yield (IPFY), is linearly proportional to the x-ray absorption cross-section without any corrections due to saturation or self-absorption effects. We demonstrate this technique on the Cu L and Nd M absorption edges of the high-Tc cuprate LNSCO by measuring the O K PFY and comparing the total electron yield, total fluorescence yield and IPFY spectra.