To elucidate the high external quantum efficiency observed for organic light-emitting diodes using a bisanthracene derivative (BD1), non-radiative transition processes as well as radiative ones are discussed employing time-dependent density functional theory. It has been previously reported that the observed high external quantum efficiency of BD1 cannot be explained by the conventional thermally activated delayed fluorescence involving T1 exciton nor triplet-triplet annihilation. The calculated off-diagonal vibronic coupling constants of BD1, which govern the non-radiative transition rates, suggest a fluorescence via higher triplets (FvHT) mechanism, which entails the conversion of a high triplet exciton generated during electrical excitation into a fluorescent singlet exciton. This mechanism is valid as long as the relaxation of high triplet states to lower states is suppressed. In the case of BD1, its pseudo-degenerate electronic structure helps the suppression. A general condition is also discussed for the suppression of transitions in molecules with pseudo-degenerate electronic structures.