The synthesis and characterization of the novel 24,29-dimethyl-6,7,15,16-tetraoxotetracyclo-[19.5.5.0(5,8).0(14,17)]-1,4,9,13,18,21,24,29-octaazaenatriaconta-Delta(5,8),Delta(14,17)-diene (L) are reported. Molecule L incorporates two squaramide functions in a overstructured chain connecting two opposite nitrogen atoms of the Me(2)[12]aneN(4) polyaza macrocyclic base to obtain a cage topology. The basicity and binding properties of L towards Cu(II) were determined by means of potentiometric measurements in aqueous solution (298.1+/-0.1 K, I=0.15 mol dm(-3)). Molecule L behaves as a diprotic base under the experimental conditions employed and forms only mononuclear Cu(II) complexes in which the squaramide moieties are not involved in the stabilization of the metal ion that is stabilized by the amine functions of the polyaza base inside the three-dimensional cavity. The [CuL](2+) species was tested as a host for the series of halide anions. UV-visible spectrophotometric experiments permitted the determination of the addition constants of halides to the Cu(II)-complexed species. The [CuL](2+) species binds the anions F(-), Cl(-), and Br(-) by forming the [CuLX](+) species, but does not bind the biggest I(-) anion. A trend of selectivity as a function of the hydrogen-bonding capability as well as the dimensions of the anion were established; the maximum value of selectivity was for addition of the F(-) anion (log K=4.8). This selectivity is due to the presence of the overstructured chain containing the squaramide groups up to the Me(2)[12]aneN(4) macrocyclic base. The squaramide groups, by providing hydrogen-bond contacts, permit the [CuL](2+) species to selectively bind these anions through the formation of a hydrogen-bond network with F(-) and Cl(-). The crystal structures of the [CuLF](+) and [CuLCl](+) cations support the results obtained in aqueous solution.