  The B-mode polarization of the cosmic microwave background (CMB) radiation is
an excellent information channel for the detection of relic gravitational
waves. However, the detection is contaminated by the B-mode polarization
generated by some other effects. In this paper, we discuss the contaminations
caused by the cosmological birefringence, which converts the CMB E-mode to the
B-mode, and forms the effective noise for the detection of gravitational waves.
We find that this contamination is significant, if the rotation angle is large.
However, this kind of B-mode can be properly de-rotated, and the effective
noises can be greatly reduced. We find that, comparing with the contaminations
caused by cosmic weak lensing, the residual polarization generated by the
cosmological birefringence is negligible for the detection of relic
gravitational waves in the CMB.
