Tetramethyleneethane (TME) is a triplet non-Kekule molecule that is currently the source of a difference between theory and experiment. The best theory places the energy of the triplet about 1 kcal/mol below the singlet at an angle of twist of 50-degrees about the central carbon-carbon bond. However, the triplet ESR spectrum shows no splitting between the x- and y-lines, indicating that the zero field parameter, E, is 0 or very small. If it is the former, that would be consistent with a D2d configured TME. In order to explore this point by removing proton hyperfine coupling, TME-d8 was prepared. Again, no splitting was observed between the x-and y-lines for TME-d8. This sets an upper limit for E of approximately 0.001 cm-1.