Recently it has been shown how the measured partial structure factors for diatomic molecular liquids might be used to generate a detailed view of the local intermolecular orientational correlation function, via the standard spherical harmonic expansion. The present work generalizes this analysis to the case of molecules of arbitrary shape. An analysis of the measured atom-atom partial structure factors for liquid water is presented, and the corresponding maps of the orientational correlation function between water molecules are derived. It is seen that this method of presenting diffraction data is rich in detail about the nature of the short-range interactions between water molecules in the liquid state. In particular, it is found that while there is a pronounced directionality in the organization of neighboring molecules around any given molecule at the origin, corresponding to the hydrogen bonding in the liquid, there are nonetheless a range of local orientations compatible with the neutron data. This argues against the notion of water forming short lived, "icelike" clusters at ambient temperature and pressure, as has been speculated in the past. The general implications for this kind of analysis for other molecular liquids, solutions, and mixtures is discussed.