Based on the normalized elimination of the small component relativistic formalism, a new approach to the calculation of hyperfine structure parameters of paramagnetic molecules is developed and implemented. The new method is tested in the calculation of the isotropic hyperfine structure constant for a series of open-shell molecules containing mercury. The results of calculations carried out in connection with ab initio methods of increasing complexity demonstrate the high accuracy of the formalism developed. In view of its computational simplicity, the new approach provides the basis for an efficient and accurate calculation of the HFS parameters of large molecules.