  The constraints on the time variation of the fine structure constant at
recombination epoch relative to its present value, $\Delta\alpha/\alpha \equiv
(\alpha_{\mathrm{rec}} - \alpha_{\mathrm{now}})/\alpha_{\mathrm{now}}$, are
obtained from the analysis of the 5-year WMAP cosmic microwave background data.
As a result of Markov-Chain Monte-Carlo analysis, it is found that, contrary to
the analysis based on the previous WMAP data, the mean value of
$\Delta\alpha/\alpha=-0.0009$ does not change significantly whether we use the
Hubble Space Telescope (HST) measurement of the Hubble parameter as a prior or
not. The resultant 95% confidence ranges of $\Delta\alpha/\alpha$ are $-0.028 <
\Delta\alpha/\alpha < 0.026$ with HST prior and $-0.050 < \Delta\alpha/\alpha <
0.042$ without HST prior.
