The rotational fine structure of the vibrationless 0(0)(0) band of the electronic S-1<--S-0 transition of glyoxal in large superfluid He-4 droplets ((N) over bar (4)=2.10(3)-2.10(4)) has been interrogated with high resolution laser depletion spectroscopy. In the electronic ground singlet state S-0 the rotational constants A and (B) over bar=(B+C)/2 are less than for the free molecule by a factor of 2.87 and 2.16, respectively. In the electronic excited state S-1 the rotational constant A is found to be 17% larger and the average rotational constants (B) over bar to be 25% smaller than in the S-0 state. The unexpected large magnitudes and different signs in the observed changes are attributed to modifications in the shape of the outer electron density distribution of the molecule upon excitation. None of the previous models introduced to explain the changes in rotational constants is entirely satisfactory, presumably because of the much weaker interactions with the helium environment.