Topological Weyl semimetals represent a novel class of non-trivial materials, where band crossings with linear dispersions take place at generic momenta across reciprocal space. These crossings give rise to low-energy properties akin to those of Weyl fermions, and are responsible for several exotic phenomena. Up to this day, only a handful of Weyl semimetals have been discovered, and the search for new ones remains a very active area. The main challenge on the computational side arises from the fact that many of the tools used to identify the topological class of a material do not provide a complete picture in the case of Weyl semimetals. In this work, we propose an alternative and inexpensive, criterion to screen for possible Weyl fermions, based on the analysis of the band structure along high-symmetry directions in the absence of spin-orbit coupling. We test the method by running a high-throughput screening on a set of 5455 inorganic bulk materials and identify 49 possible candidates for topological properties. A further analysis, carried out by identifying and characterizing the crossings in the Brillouin zone, shows us that 3 of these candidates are Weyl semimetals. Interestingly, while these 3 materials underwent other high-throughput screenings, none had revealed their topological behavior before.