We have studied the resonant elastic scattering reaction Ne+p in reverse kinematics, by using the intense (4 × 10 pps) Ne radioactive beam at the Centre de Recherches du Cyclotron RIB facility at Louvain-la-Neuve. The recoil protons were detected at 20 different angles in the LEDA segmented silicon detector. The resulting elastic scattering cross sections have been analysed using the R-matrix method. We have observed for the first time the second excited state (J = 1/2, ℓ = 0) of the proton-rich nucleus Na at the center-of-mass energy E = 1.066 ± 0.003 MeV with a proton width Γ = 101 ± 3 keV. The Coulomb shift between the 1/2 mirror levels in O and Na is 0.73 MeV, among the largest values currently observed in light exotic nuclei.