This letter presents a new method of digital adaptive pre-distortion for linearization of power amplifiers (PA). The method is derived from a post-distortion approach which identifies the PA inverse function. This approach leads to the minimization of a quadratic function of the polynomial coefficients in the case of a polynomial predistorter form and a least square criterion. We have compared our solution to a method previously proposed by Ghaderi (1996) that was also based on the transformation of a post-distortion into a pre-distortion system. We have tested our predistorter (along with a baseband adaptation of Ghaderi's) on OFDM Hiperlan signals. Both methods significantly reduced the signal distortion and the spectral regrowth. Our less complex approach proved to be even better for small peak back off values.