The paper reports the first experimental observation of effective hydrodynamic screening in charged colloidal suspensions. A unique combination of dynamic x-ray scattering, cross -correlated dynamic light scattering, and small angle x-ray scattering is used. This new combination of techniques is cardinal to obtain the collective diffusion coefficient and the static structure factor simultaneously, free from multiple scattering effects, over a sufficiently wide range of wave vectors. This allows the determination of the hydrodynamic function on optically strongly scattering samples purely experimentally, free from any modeling of the dynamic or static properties. The multiple-scattering free experimental techniques used give complete freedom to change the properties of the solvent and thus vary the range and strength of the electrostatic repulsion between the colloids. Doing so, one observes a strong influence of the structure on the hydrodynamic interactions. For samples with relatively weak interparticle structuring, the data agree reasonably well with fluctuation expansion calculations. As the range of the direction interaction increases and static density correlations become stronger, however, one finds large deviations from this theory. The results show that higher-order many body effects in dense, charge stabilized colloidal suspensions, that are beyond the scope of current theories, lead to a flattening of the hydrodynamic function. Phenomenologically, this flattening can be described as hydrodynamic screening.