  Tight binding electrons on the honeycomb lattice are studied where nearest
neighbor hoppings in the three directions are $t_a,t_b$ and $t_c$,
respectively. For the isotropic case, namely for $t_a=t_b=t_c$, two zero modes
exist where the energy dispersions at the vanishing points are linear in
momentum $k$. Positions of zero modes move in the momentum space as $t_a,t_b$
and $t_c$ are varied. It is shown that zero modes exist if $||\frac{t_b}{t_a}|
-1| \leq |\frac{t_c}{t_a}| \leq ||\frac{t_b}{t_a}|+1|$. The density of states
near a zero mode is proportional to $|E|$ but it is propotional to $\sqrt{|E|}$
at the boundary of this condition.
