The HDO/H2O abundance ratio is thought to be a key diagnostic for the evolution of water during the star and planet formation process and thus for its origin on Earth. We here present millimeter-wavelength high angular resolution observations of the deeply embedded protostar NGC 1333-IRAS4B from the Submillimeter Array targeting the 312-221 transition of HDO at 225.6 GHz (Eu = 170 K). We do not (or only very tentatively) detect the HDO line toward the central protostar, contrasting the previous prominent detection of a line from another water isotopologue, H18 2O, with similar excitation properties using the IRAM Plateau de Bure Interferometer. The non-detection of the HDO line provides a direct, model-independent, upper limit to the HDO/H2O abundance ratio of 6 × 10-4 (3s) in the warm gas associated with the central protostar. This upper limit suggests that the HDO/H2O abundance ratio is not significantly enhanced in the inner ˜50 AU around the protostar relative to what is seen in comets and Earth's oceans and does not support previous suggestions of a generally enhanced HDO/H2O ratio in these systems.