A dyad of orthogonally arranged chromophores of benzoperylenehexacarboxylictrisimide (energy donor, D) and terrylenetetracarboxylic bisimide (energy acceptor, A) was synthesized where a quantitative energy transfer (FRET) from D to A was found, although not only are both transition moments orthogonally arranged but the spectral overlap between the fluorescence of the energy donor and the absorption of the acceptor is also small. Even an appreciable further diminishing of the overlap in a dyad with phenylbenzoxazole as the donor could not inhibit the energy transfer. Thus, the application of the FRET theory to real systems is estimated to be limited where molecular vibrations seem to play a key role in the energy transfer.