The interaction of a neutral squaramide-based receptor, equipped with two 4-nitrophenyl substituents (Rsq), with halides and oxoanions has been studied in MeCN. UV/Vis and 1H NMR spectroscopy titration experiments clearly indicated the formation of 1:1 hydrogen bonding [Rsq⋅⋅⋅X]+ complexes with all the investigated anions. X-ray diffraction studies on the chloride and bromide complex salts confirmed the 1:1 stoichiometry and indicated the establishment of bifurcated hydrogen-bond interactions between the squaramide-based receptor and the halide anion that involved both 1) amide NH and 2) aryl proximate CH fragments, for a total of four bonds. Probably due to the contribution of CH fragments, complexes of Rsq with halides are 1 to 2 orders of magnitude more stable than the corresponding ones with the analogous urea-based receptor that contains two 4-nitrophenyl substituents (Rur). In the case of oxoanions, Rsq forms complexes, the stability of which decreases with the decreasing basicity of the anion (H2PO4−>NO2−≈HSO4−>NO3−), and is comparable to that of complexes of the urea-based receptor Rur. Such a behaviour is ascribed to the predominance of different contributions: electrostatic interaction for halides, acid-to-base ‘frozen’ proton transfer for oxoanions. Finally, with the strongly basic anions F− and CH3COO−, Rsq first gives genuine hydrogen-bond complexes of 1:1 stoichiometry; then, upon addition of a second anion equivalent, it undergoes deprotonation of one NH fragment, with the simultaneous formation of the dianion hydrogen-bond complexes, [HF2]− and [CH3COOH⋅⋅⋅CH3COO]−, respectively. In the case of the urea-based derivative Rur, deprotonation takes place with fluoride but not with acetate. The apparently higher Brønsted acidity of Rsq with respect to Rur reflects the capability of the squaramide receptor to delocalise the negative charge formed on NH deprotonation over the cyclobutene-1,2-dione ring and the entire molecular framework.