  Eigenvalues of the Breit Equation {eqnarray*} [(\vec{\alpha}_{1} \vec{p} +
\beta_{1}m)_{\alpha \alpha^{\prime}} \delta_{\beta \beta^{\prime}} +
\delta_{\alpha \alpha^{\prime}} (-\vec{\alpha}_{2} \vec{p} + \beta_{2}M)_{\beta
\beta^{\prime}} - \frac{e^{2}}{r} \delta_{\alpha \alpha^{\prime}} \delta_{\beta
\beta^{\prime}}] \Psi_{\alpha^{\prime} \beta^{\prime}} = E \Psi_{\alpha \beta},
{eqnarray*} in which only the static Coulomb potential is considered, have been
found. Here the detailed discussion on the simple caces, $^{1}S_{0},\ m=M$ and
$m \neq M$ is given deriving the exact energy eigenvalues. The $\alpha^2$
expansion is used to find radial wave functions. The leading term is given by
classical Coulomb wave function. The technique used here can be applied to
other cases.
