The renormalization group theory is applied to the determination of localized phonons in a finite size two dimensional monolayer. The fixed-point equation defines the critical values of the adsorbate-substrate force constants leading to the occurrence of localized modes. The transformation equation near the fixed point gives scaling laws and critical exponents which characterize the asymptotic behavior of the localization length of the phonons. (C) 2000 American Institute of Physics. [S0021-9606(00)70609-X].