Complexation of 4,6-bis{3-(2-pyridyl)-1H-pyrazol-1-yl}pyrimidine (bppp) and copper(II) tetrafluoroborate in methanol gave a self-assembled [Cu2(CH3O)2(bppp)2]2+ ion having a betweenanene-type structure. Each bppp spans across the common Cu2O2 plane in a trans fashion to ligate each copper center. The antiferromagnetic interaction observed in the Cu2O2 core is ascribable to the superexchange along the Cu-O-Cu linkage and found to be one of the largest among the analogous compounds, owing to the large Cu-O-Cu angle perturbed with the two bppp molecular tweezers.