We present the results of our study about a newly discovered asteroid family in the inner main belt: the primordial S-type family. From an initial list of 263 asteroids that are considered as potential members of the aforementioned primordial family, we retrieved their spectra in visible and near infrared range from the literature and from the Gaia DR3 spectral catalog of solar system objects. For asteroids having no or poor signal-to-noise ratio spectra in the literature, we carried out new ground-based observations. We obtained new spectra for 33 members of the family using the 1.82m Asiago telescope for the visible spectroscopy, while for near infrared spectroscopy we used the 3.58m Telescopio Nazionale Galileo (TNG) and the 4.30m Lowell Discovery Telescope (LDT). In total, we collected spectra of 261 potential members of the primordial S-type family out of 263. We determined their spectral taxonomy and properties, such as spectral slopes and absorption bands parameters, when existing. Using the taxonomical characterization and the orbital space parameters, we identified and removed 71 interlopers from the potential members list. The final list of the primordial S-type family members includes 190 asteroids.