  Flavor SU(3) analysis of heavy meson ($B$ and $D$) hadronic charmless decays
can be formulated in two different ways. One is to construct the SU(3)
irreducible representation amplitude (IRA) by decomposing effective Hamiltonian
according to the SU(3) transformation properties. The other is to use the
topological diagrams (TDA). These two methods should give equivalent physical
results in the SU(3) limit. Using $B \to PP$ decays as an example, we point out
that previous analyses in the literature using these two methods do not match
consistently in several ways, in particular a few SU(3) independent amplitudes
have been overlooked in the TDA approach. Taking these new amplitudes into
account, we find a consistent description in both schemes. These new amplitudes
can affect direct CP asymmetries in some channels significantly. A consequence
is that for any charmless hadronic decay of heavy meson, the direct CP symmetry
cannot be identically zero.
