This study presents the first results of a deconvolution method for Liquid Scintillation complex spectra. The method has been developed by means of the software MATLAB and is based on the utilization of Fourier Transforms. Its main target is to obtain a fast calculation procedure capable to unfold complex spectra without requiring any preliminary knowledge of the peak shapes of the component nuclides. Experimental tests have been carried out by means of a Perkin Elmer Wallac Quantulus 1220. Distinctive features of Quantulus have not been used, the instrument was only utilized to generate spectra in numerical form that subsequently were uploaded to a PC and analyzed by MATLAB. Results show acceptable capabilities of the method both for fitting convoluted spectra and for unfolding single nuclide shapes. Further experimentation is scheduled, in order to take account of quenching effects; it will be carried out by adding to the calculation algorithm another step, capable of performing a self-choice of the number of harmonics. The final aim is to fit any kind of beta spectra also when quenching influences the shape deeply.