  The radiative corrections to the pure leptonic decay $D_s{\longrightarrow}
{\ell}{{\nu}}_{\ell}$ up-to one-loop order is presented. We find the virtual
photon loop corrections to $D_s{\longrightarrow} {\tau}{{\nu}}_{\tau}$ is
negative and the corresponding branching ratio is larger than $3.51\times
10^{-3}$. Considering the possible experimental resolutions, our prediction of
the radiative decay $D_s{\longrightarrow} {\tau}{{\nu}}_{\tau}\gamma$ is not so
large as others, and the best channel to determine the $V_{cs}$ or $f_{D_s}$ is
$D_s{\longrightarrow} {\mu}{{\nu}}_{\mu}{\gamma}$. How to cancel the infrared
divergences appearing in the loop calculations, and the radiative decay
$D_s{\longrightarrow} {\ell}{{\nu}}_{\ell}{\gamma}$ is shown precisely. It is
emphasized that the radiative decay may be separated properly and may compare
with measurements directly as long as the theoretical `softness' of the photon
corresponds to the experimental resolutions.
