Si3N4 has become an important material with great technological and scientific interests. The lattice symmetry and the crystallinity quality of Si3N4 thin films are fundamental parameters that must be determined for different applications. In order to evaluate the properties of Si3N4 films, we used reflectance difference spectroscopy/reflectance anisotropy spectroscopy (RDS/RAS) to measure the optical anisotropy of Si3N4 thin films (1-2 nm) grown by nitridation of two different Si(111) substrates, one with a 4.2° miscut off towards the  direction and another one with a nonintentional miscut. We demonstrate that, by modifying the measurement optical setup, we could increase the RD sensitivity and clearly display the optical response corresponding to the hexagonal symmetry of the Si3N4 thin layer. Our results are in good agreement with reflection high energy electron diffraction (RHEED) measurements for both misoriented and oriented substrates.