Artifacts made of cellulose, such as ancient documents, pose a significant experimental challenge in the THz transmission spectra interpretation due to their small optical thickness. In this Letter we describe a method to recover the complex refractive index of cellulose fibers from the THz transmission data obtained on single freely standing paper sheets in the 0.2-3.5 THz range. By using our technique, we were able to eliminate Fabry-Perot effects and recover the absorption coefficient of the cellulose fibers. The obtained THz absorption spectra are explained in terms of absorption peaks of the cellulose crystalline phase superimposed to a background contribution due to a disordered hydrogen bonds network. The comparison between the experimental spectra with THz vibrational properties simulated by density functional theory calculations confirms this interpretation. In addition, evident changes in the THz absorption spectra are produced by natural and artificial aging on paper samples, whose final stage is characterized by a spectral profile with only two peaks at about 2.1 THz and 3.1 THz. These results could be used to provide a quantitative assessment of the state of preservation of cellulose artifacts.