  The color superconducting phase of two-flavor quark matter is studied under a
Fierz-transformed Lagrangian. In the Fierz-transformed Lagrangian both the
quark-antiquark and quark-quark channel are included. Two parameters $\alpha$
and $\beta$ are introduced to weight the Fierz-transformed quark-antiquark
Lagrangian and quark-quark Lagrangian, respectively. The couplings of different
interaction channel are thus fixed by the two coefficients other than five free
parameters. The interplay between chiral symmetry restoration and the formation
of color superconducting phases are discussed. It is found that the increase of
$\alpha$ leads the chiral phase transition from first order to crossover. The
calculated specific heat shows jump at critical temperature which confirms the
phase transition. The increase of $\beta$ leads the pseudo-critical chemical
potential reduce. With large $\beta$ the superconductors gap $\Delta$ can be
larger than the typical value and the well-known BCS relation between critical
temperature and gap is well fitted.
