  We present a condition for automatic O$(a)$ improvement in twisted mass
lattice QCD, using symmetries of the Symanzik effective theory. If the
continuum part of the Symanzik effective theory is invariant under a particular
transformation, named $T_1$ in this report, scaling violations of all
quantities invariant under $T_1$ transformation are even in the lattice spacing
$a$. On the other hand, quantities non-invariant under $T_1$ vanish in the
continuum limit with odd powers in $a$. We prove this statement even for the
massive case without using the equation of motion. We also consider a few
different criteria for the $T_1$ invariant condition in lattice theories and
discuss ambiguities of the lattice condition for O$(a)$ improvement.
