The O-17 NQR frequencies have been measured in cis-cyclobutane-1,2-dicarboxylic acid and the quadrupole coupling tensors have been determined at various temperatures. Two O center dot center dot center dot H oxygen positions and two O-H oxygen positions are observed, showing the presence of two different types of O-H center dot center dot center dot O hydrogen bonds in the unit cell. The quadrupole coupling constants at the O-H oxygen positions are approximately 30% lower than the lowest quadrupole coupling constants experimentally observed at the C-O-H positions in other carboxylic acids with either ordered or disordered hydrogen bonds. The O-H distances have been calculated from the O-17-H-1 dipole dipole interaction at the O-H oxygen positions. The obtained values are longer than the O-H distances usually found in O-H center dot center dot center dot O hydrogen bonds with comparable O center dot center dot center dot O distance, in agreement with the proposed proton exchange O-H center dot center dot center dot O <-> O center dot center dot center dot H-O, which partially averages the dipole-dipole interaction. The energy difference of the two proton configurations, O-H center dot center dot center dot O and O center dot center dot center dot H-O, is calculated from the O-H distances determined by NQR. The temperature dependence of the O-17 quadrupole coupling tensors at the O-17 center dot center dot center dot H-O oxygen positions is analyzed in the model of proton exchange and the energy differences of the two proton configurations obtained by this analysis agree with the values obtained from the O-H distances. The quadrupole coupling tensors are analyzed in a model based on the Townes and Dailey model. The model shows that the population of an oxygen lone pair orbital is at this oxygen position reduced from 2 to approximately 1.3. The electron electric charge is most probably transferred to the oxygen sigma and pi electron orbitals. This may be associated with the structure of the cyclobutane ring, where the X-ray data show the presence of two unusually short C-C bonds.