This study presents a novel spatial discretization for the compressible Euler equations that enforces discrete entropy conservation when an arbitrary equation of state is used. The strategy for deriving this results, which still guarantees the discrete conservation of mass, momentum and total energy as well as the preservation of the kinetic energy by its convective term, relies on the manipulation of the main balance equations and the imposition of the global conservation of entropy, that is assured at a continuous level when a nonviscous, discontinuity-free flow field is assumed. The proposed formulation, which admits a high-order extension, is assessed through numerical tests performed in transcritical and supercritical conditions with some of the most popular cubic equations of state.