  The stability of the zero-energy Landau levels in bilayer graphene against
the chiral symmetric disorder is examined in the presence of the trigonal
warping. Based on the tight-binding lattice model with a bond disorder
correlated over several lattice constants, it is shown that among the four
Landau levels per spin and per valley, two Landau levels exhibit the anomalous
sharpness as in the absence of the trigonal warping, while the other two are
broadened, yielding split peaks in the density of states. This can be
attributed to the fact that the total chirality in each valley is +2 or -2,
which is protected topologically even in the presence of an intra-valley
scattering due to disorder.
