Decays of individual rovibronic levels of trans-glyoxal in its first excited singlet state are investigated in supersonic-jet conditions. Several rotational levels display oscillatory decay from coherent excitation of superposition of singlet and triplet states. Analysis yields a lower bound for the state-dependent coupling matrix elements upsilon(ST)=0.08-62 MHz for the S-1-T-1 interaction. These matrix elements of the lowest singlet and triplet states show no simple systematic dependence on vibrational states, but the singlet state at greater K quantum number couples to a few triplet states with upsilon(ST) larger than for the state at lower K. The complex beat pattern is explored on varying the polarization of the laser beam relative to an external magnetic field. For state N-KaKc=3(12) at excitation energy 25 254.36 cm(-1), the Lande g factor of its coupling triplet hyperfine levels is estimated. From comparison with the theoretical g value for the Hund's case (b), we found that for this state rotational angular momentum is conserved during singlet-triplet coupling. Irregular M-F splittings and correlated beating frequencies resulting from resonance coupling between the singlet and triplet states are observed in the Fourier-transform spectra under the weak magnetic field condition.