Nematic phases, despite being unknown to the general population, are found in many natural systems. However, if quantum magnets can also achieve such an order is yet unclear. Spin-nematic states are defined by multiple-spin order and thus lack the conventional dipolar long-range magnetic ordering, which is why firm experimental evidence is still missing. A system that has drawn considerable attention is a zigzag spin-1/2 chain, with competing ferromagnetic nearest-neighbor, J1, and antiferromagnetic next-nearest neighbor, J2, interactions. Here, the spin-nematic phase is predicted to occur in the applied magnetic field close to the saturation. However, high saturation fields (>40 T) of the existing compounds severely reduce applicable experimental techniques and thus hinder the search for the spin-nematic phase. We propose a neutron diffraction study of a new realization of the J1-J2 chain model, b-TeVO4, where saturation fields of ~22 T is within the reach of the HZB HFM magnet.