While hydrogen could be an important light alloying element in planetary iron cores, phase relations in the Fe‐FeH system remain largely unknown at high pressures and temperatures (P‐T). A speculative Fe‐H2 phase diagram has been proposed assuming continuous solid solution between Fe and FeH and eutectic melting between FeH and H2. Recent studies revealed that stoichiometric FeH becomes non‐magnetic above ∼40 GPa, which might affect its melting behavior. Here we examined the melting curve of non‐magnetic FeH between 43 and 152 GPa by a combination of laser‐heated diamond‐anvil cell techniques and synchrotron X‐ray diffraction (XRD) analyses. The melting temperature was determined by employing the appearance of additional hazy XRD signals upon quenching temperature as a melting criterion. We also performed thermodynamic modeling, which well reproduces the change in the curvature of FeH melting curve upon the loss of magnetism and extrapolates the experimental constraints to inner core pressures. The XRD data showed that non‐magnetic FeH melts congruently at temperatures higher than the known eutectic melting curve for FeHx (x > 1). Combined with the fact that the endmembers exhibit different crystal structures, these results indicate that Fe and non‐magnetic FeH form a eutectic system. The dT/dP slope of the FeH melting curve is comparable to that for Fe, suggesting that the eutectic liquid composition of FeH0.42 (Fe + 0.75 wt% H) previously estimated at ∼40 GPa changes little with increasing pressure. Plain Language Summary: It is likely that a large amount of water was transported to the Earth during its accretion and hydrogen was incorporated into core‐forming metals. Indeed, recent calculations found that hydrogen could be an important light element in both the outer and inner core to explain the observed density and velocities. Nevertheless, experimental study of Fe‐H alloys has been challenging, in part because hydrogen is almost insoluble in iron at 1 bar. Here we determined the melting curve of stoichiometric FeH in the non‐magnetic state from 43 to 152 GPa based on X‐ray diffraction (XRD) measurements. The melting temperature of FeH increases rapidly with compression upon the loss of local spin moment. The XRD spectra show that stoichiometric FeH melts congruently, suggesting eutectic melting between Fe and FeH that is supported by the different crystal structures between these two endmembers. Since the dT/dP slopes of the Fe and FeH melting curves are similar, it is likely that the Fe‐FeH eutectic liquid composition is little dependent on pressure and could be around FeH0.42 at inner core conditions, which gives the upper bound for the hydrogen concentration in the outer core. Key Points: We determined the melting curve of non‐magnetic FeH to 152 GPa based on synchrotron X‐ray diffraction (XRD) measurementsXRD data indicated congruent melting of non‐magnetic FeH, suggesting eutectic melting between Fe and FeH above ∼40 GPaSimilar dT/dP slopes between the melting curves of Fe and FeH imply little pressure dependence of the Fe‐FeH eutectic liquid composition [ABSTRACT FROM AUTHOR]