  It is shown that the phase diagram of the two-dimensional generalized
fully-frustrated XY model on a square lattice contains a crossing of the
chirality transition and the Kosterlitz-Thouless (KT) transition, as well as a
stable phase characterized by a finite helicity modulus $\Upsilon$ and an
unbroken chirality symmetry. The crossing point itself is consistent with a
critical point without any jump in $\Upsilon$, with the size ($L$) scaling $%
\Upsilon\sim L^{-0.63}$ and the critical index $\nu\approx0.77$. The KT
transition line remains continuous beyond the crossing but eventually turns
into a first-order line. The results are established using Monte-Carlo
simulations of the staggered magnetization, helicity modulus, and the
fourth-order helicity modulus.
