[en] Calculations of Slater-Koster (SK) parameters appearing in the tight-binding method using sp³d⁵ basis sets for both the cationic and anionic species are presented for ZnS and CdS. We have adjusted these parameters to match the band structures obtained from the full potential linear augmented plane wave method. This operation has been carried out for a variety of structures namely zinc blende, wurtzite, rocksalt, CsCl and for a wide range of near-neighbor distances. The SK parameters have slightly different values for the same near-neighbor distance in different structures. Therefore, a least-squares fitting has been performed separately for each parameter as a function of only the near-neighbor distance to guarantee the transferability of these parameters to different structural environments. The fitted parameters are then used to calculate the electronic structure of small-sized clusters of ZnS and CdS in given geometries and the results are compared with ab initio results. A fairly good agreement found in the one-electron energy spectrum and total energy confirms transferability of the parameters to different length scales. A detailed account of the calculation procedure and calibration results is given in the present paper. These parameters can be used to study the electronic structure of large-sized clusters where first-principles methods are computationally demanding. It may be mentioned that the SK parameters do not satisfy the R^-(l+l'+1) Harrison scaling law for larger values of the near-neighbor distance R.