  We investigate the hyperon bulk viscosity due to the non-leptonic process $n
+ p \rightleftharpoons p + \Lambda $ in $K^-$ condensed matter and its effect
on the r-mode instability in neutron stars. We find that the hyperon bulk
viscosity coefficient in the presence of antikaon condensate is suppressed
compared with the case without the condensate. The suppressed hyperon bulk
viscosity in the superconducting phase is still an efficient mechanism to damp
the r-mode instability in neutron stars.
