In a previous article [J. Chem. Phys. 57, 2684 (1972)] sufficient conditions were established for the existence of the dielectric constant ɛ in rigid-dipole fluids. One of these conditions was an unrealistic restriction on the angular dependence of the direct correlation function c (12) at short range. Here it is shown that this restriction can be removed without altering the previous conclusions. Consequently, ɛ rigorously exists if c (12) depends only upon relative positions and orientations of molecules 1 and 2, and becomes asymptotic to -φd(12)/kT at long range, where φd(12) is the dipole-dipole potential. The development is based upon the functional-derivative interpretation of c (12) in terms of the response of the single-molecule distribution function to a single-molecule external field. The consequences of formally separating c (12) and the total correlation function h (12) into short- and long-range parts are briefly explored. A relation between the angular moments of the short-range parts of c (12) and h (12) is derived in an appendix.