  The electric/color neutral solution and the critical conditions for gapless
formation are investigated in the $K^0$ condensed color-flavor locked matter.
We point out that there exist no longer gapless modes for down-strange quark
pairing while the gapless phenomenon for up-strange one is dominated in the
$K^0$ condensed environment. In a model-independent way, the phase transition
to the resulting gapless phase is found to be of first-order. The novel phase
structure implies that the chromomagnetic instability happens in the
previous-predicted gapless phase might be removed at least partly.
