  The one dimensional dimer model is investigated and the localization length
calculated exactly. The presence of delocalized states at $E_c =
\epsilon_{a,b}$ of two possible values of the chemical potential in case of
$\mid\epsilon_a-\epsilon_b\mid \leq 2 $ is confirmed and the corresponding
indices of the localization length were calculated. The singular integral
equation connecting the density of states with the inverse localization length
is solved and the analytic expression for the density of states compared with
the numerical calculations.
