The radial distribution function (RDF) of liquid water has been determined by x-ray scattering. Using a free-standing water jet and a diffracted beam analyzer to separate the Compton from the elastic scattering experimentally, several significant sources of error have been eliminated in the experiment. These have enabled the collection of quality data out to 19.7 A(-1). Data were collected both at 278 K and at 296 K. Our RDF presents fine structure, particularly, a distinct peak at 3.4 A and a peak split at 4.5 A. These features cannot be interpreted by a simple tetrahedral configuration suggested by continuum models. The uncertainties due to the truncation effects and the choice of scattering factors are found to have little influence on the RDF at intermolecular distances.