Melt ¼ cup butter. Stir in the flour to make a smooth paste. Add paprika and salt. Mix well. Add the water and let come just to the boiling point.
Just before serving, while still warm, add the last ¼ cup butter, cut into small pieces. Beat the butter pieces gradually into the mixture until they disappear from the surface.
Serve over fish which has a very pronounced flavor of its own, not on bland fish which needs a distinctively flavored sauce.