  We consider some radiative corrections to the lowest order annihilation
diagram for the orthopositronium decay rate. The insertion of the renormalized
vertex correction in the annihilation graph gives $1.6283 (\alpha/\pi)^2
\Gamma_0$. We compute also the contribution of the square of the lowest order
annihilation amplitude, which turns out to be $0.1702 (\alpha/\pi)^2 \Gamma_0$.
Finally, we obtain a term $\alpha^2 \ln\alpha \Gamma_0$ arising from the
correction to the light-light scattering block due to the exchange of one
coulombic photon, in agreement with earlier computations.
