AbstractBlack hole X-ray binaries with large mass ratios and short orbital periods are expected to change their orbital period due to magnetic breaking, mass loss, gravitational radiation, or mass evaporation of the black hole in alternative descriptions of gravity, like in braneworld gravity scenarios.The black hole X-ray binary XTE J1118+480, consisting of a late-type secondary star orbiting a ~ 8 M_⊙ black hole in a 4.1-hr period, offers a unique opportunity to test these models. New spectroscopic data allow us to determine the time of the inferior conjunction of the secondary star at different epochs. Observations over a 10 year span will provide constraints on the rate of any orbital period change.We present here a preliminary radial velocity curve obtained with the 10.4m GTC telescope equipped with OSIRIS medium-resolution spectrograph, as part of an ongoing long-term program to study the orbital period evolution in this binary.