  We formulate and prove the archimedean period relations for Rankin-Selberg
convolutions for $\mathrm{GL}(n)\times \mathrm{GL}(n-1)$. As a consequence, we
prove the period relations for critical values of the Rankin-Selberg
L-functions for $\mathrm{GL}(n)\times \mathrm{GL}(n-1)$ over arbitrary number
fields.
