Jet-cooled trans-glyoxal molecules were excited in the S-1(1) <-- S-1(0) transition using a pulsed, narrow-band (0.10-cm(-1)) dye laser. Collision-free conditions were ensured using a large nozzle-laser beam distance (27 mm) and low stagnation pressures (similar to 80 Torr). Spectrally unresolved fluorescence was observed with a photomultiplier viewing either the excitation region itself or a region of the molecular beam well downstream (46 mm) from the laser beam. Respectively, detection time windows of 0-6 and 30-80 mu s after the laser pulse were used. In the latter case, the signal intensity was similar to 2 x 10(-3) of the farmer. This is at least 100 times greater than calculated from the known S-1 glyoxal fluorescence lifetime (2.4 mu s). However, only certain isolated rovibronic levels exhibit this anomalously slow fluorescence. The rotationally resolved excitation spectra of 17 S-1 <-- S-0 bands were recorded both in the "slow" and "prompt" fluorescence mode. While the latter showed the usual dense line pattern, the former consisted of much fewer distinct lines, their number increasing with the excess vibrational energy. The corresponding emitting levels owe their long lifetime to the partial triplet character of their wave function, due to accidental resonance with T-1-state levels. For the 0(0)(0) and 5(0)(1) S-1 <-- S-0 bands, the rotational quantum numbers of the perturbed S-1 levels were determined from a computer simulation. This is the first state-specific, collision-free observation of the previously predicted fluorescence Lifetime lengthening through intramolecular S-1/T-1 coupling in small organic molecules. It could, in fact, be shown experimentally that in previous reports on the glyoxal phosphorescence excited in the S-1 region, collisional effects must have obscured the behavior of the isolated molecules.