  We use a renormalized mean field theory to study the Gutzwiller projected BCS
states of the extended Hubbard model in the large $U$ limit, or the
$t$-$t'$-$J$-$J'$ model on a two-dimensional checkerboard lattice. At small
$t'/t$, the frustration due to the diagonal terms of $t'$ and $J'$ does not
alter the $d_{x^2-y^2}$-wave pairing symmetry, and the negative (positive)
$t'/t$ enhances (suppresses) the pairing order parameter. At large $t'/t$, the
ground state has an extended s-wave symmetry. At the intermediate $t'/t$, the
ground state is $d+id$ or $d+is$-wave with time reversal symmetry broken.
