  We study the stability of the color-flavor locked (CFL) phase of dense quark
matter with regard to the formation of a non-zero Goldstone boson current. We
show that an instability appears in the vicinity of the point $\mu_s=\Delta$
which marks the appearance of gapless fermion modes in the CFL phase. Here,
$\mu_s=m_s^2/(2\mu)$ is the shift in chemical potential due to the strange
quark mass and $\Delta$ is the gap in the chiral limit. We show that in the
Goldstone boson current phase all components of the magnetic screening mass are
real. In this work we do not take into account homogeneous kaon condensation.
We study the effects of an instanton induced interaction of the magnitude
required to suppress kaon condensation.
