  Diskoseismic c-modes in accretion discs have been invoked to explain
low-frequency variabilities observed in black-hole X-ray binaries. These modes
are trapped in the inner-most region of the disc and have frequencies much
lower than the rotation frequency at the disc inner radius. We show that
because the trapped waves can tunnel through the evanescent barrier to the
corotational wave zone, the c-modes are damped due to wave absorption at the
corotation resonance. We calculate the corotational damping rates of various
c-modes using the WKB approximation. The damping rate varies widely depending
on the mode frequency, the black hole spin parameter and the disc sound speed,
and is generally much less than 10% of the mode frequency. A sufficiently
strong excitation mechanism is needed to overcome this corotational damping and
make the mode observable.
