We suggest a novel method for systematic improvement of anharmonic adsorbate frequencies based on a fragment approach. The calculations are carried out by considering the adsorbed molecule separately and computing an energy correction using high-level ab initio method in addition to a standard calculation of the whole adsorbed system using quantum mechanical techniques with periodic boundary conditions. We demonstrate its reliability for a C2H2 molecule chemisorbed on a Cu(001) surface. We also show that the accuracy of the presented approach with a suitable description of the periodic surface depends mainly on the accuracy of the high-level ab initio method used to describe the adsorbate molecule. Moreover, our technique potentially allows to predict adsorbate vibrational spectra with spectroscopic accuracy.