The use of parahydrogen – the isomer of molecular hydrogen with zero nuclear spin – is important for promising and actively developing methods for spin hyperpolarization of nuclei called parahydrogen induced polarization (PHIP). However, the dissolved parahydrogen in PHIP experiments quickly loses its spin order, resulting in the formation of orthohydrogen and reduction of the overall nuclear polarization of the substrate. This process is due to the difference of chemical shifts of hydride protons, as well as spin–spin couplings between nuclei, in the intermediate catalytic complexes, and it has not been rigorously explained so far. We proposed a new experimental technique based on magnetic field cycling for measuring the rate of molecular hydrogen para–ortho conversion in solution and applied it for non-hydrogenative PHIP Signal Amplification By Reversible Exchange (SABRE) experiments. The para–ortho conversion rate was measured over a wide range of magnetic field from 0.5 mT to 9.4 T. It was found that the conversion rate strongly depends on the magnetic field in which the reaction occurs, as well as on the concentrations of reactants. The rate decreases with increasing the concentration of pyridine ligand and increases with increasing the concentration of iridium catalyst. The model, which takes into account the reversible exchange of molecular hydrogen with the catalyst, nuclear spin–spin interaction of hydride protons with nuclei of ligands within catalytic complex and nuclear Zeeman interactions, qualitatively describes the experimental data. Two types of complexes with different spin system symmetry contribute to the molecular hydrogen conversion. In asymmetric complexes possessing hydride protons with different chemical shifts due to the presence of chlorine anion ligand the para–ortho conversion rate increases with magnetic field, while for symmetric complexes this mechanism is not operable. In the magnetic field where level anti-crossing occurs the resonant feature for the rate of para–ortho conversion is found. The results of this work can be utilized for finding the optimal conditions for obtaining the maximum hyperpolarization in the experiments employing parahydrogen.