  Relativistic mean field theory allowing for triaxial deformations is applied
for a systematic study of fission barriers in the actinide region. Different
pairing schemes are studied in details and it is shown that covariant density
functional theory is able to describe fission barriers on a level of accuracy
comparable with non-relativistic calculations, even with the best
phenomenological macroscopic+microscopic approaches. Triaxiality in the region
of the first saddle plays a crucial role in achieving that.
