Vacuum polarization correction to the positronium decay rate

Corrections $\sim {\alpha }^2$ to the positronium decay rate, induced by one–loop vacuum polarization diagram, are calculated. Their relative values are $0.4468(3)(\alpha \mathrm{/}\pi {)}^2$ for para- and $0.960(3)(\alpha \mathrm{/}\pi {)}^2$ for orthopositronium.