The pKBHX (logarithm of complexation constant K of 4-fluorophenol with bases) hydrogen-bond basicity scale of neutral hydrogen-bond acceptors (HBAs) is extended to anionic HBAs. The scale is constructed for 26 anions through (i) the infrared measurement of K on NBu4+X- ion pairs in CCl4, (ii) the estimation of K from linear free energy relationships between measured K values and literature K values for various phenols in polar solvents, and (iii) the computation of K at the density functional theory level in CCl4. The scale extends on a 9.4 pK unit range from fluoride to tetraphenylborate. Considering a number of anions as organic functions substituted with unipolar substituents, their pKBHX values can be related to the Hammett-Taft substituent constants σ. Unipolar substituents (O- and S-) obey the same pKBHX versus σ relationships as dipolar ionic (N-N+R3) and dipolar (OH, CF3, NR2, or OR) ones for the nitrile, carbonyl, nitroso, nitro, sulfonyl, and phosphoryl functions. Like dipolar substituents, unipolar substituents at carbon and nitrogen operate by field-inductive and resonance effects, whereas substituents at sulfur and phosphorus operate only by the field-inductive effect.