The symmetry of a molecule junction has been shown to play a significant role in determining the conductance of the molecule, but the details of how conductance changes with symmetry have heretofore been unknown. Herein, we investigate a naphthalenedithiol single-molecule system in which sulfur atoms from the molecule are anchored to two facing gold electrodes. In the studied system, the highest single-molecule conductance, for a molecule junction of 1,4-symmetry, is 110 times larger than the lowest single-molecule conductance, for a molecule junction of 2,7-symmetry. We demonstrate clearly that the measured dependence of molecule junction symmetry for single-molecule junctions agrees with theoretical predictions.