  In this paper, we analyze the high-resolution UV spectra for a C1.7 solar
flare (SOL2017-09-09T06:51) observed by the \textit{Interface Region Imaging
Spectrograph} (\textit{IRIS}). {We focus on the spectroscopic observations at
the locations where the cool lines of \ion{Si}{4} 1402.8 \AA\ ($\sim$10$^{4.8}$
K) and \ion{C}{2} 1334.5/1335.7 \AA\ ($\sim$10$^{4.4}$ K) reveal significant
redshifts with Doppler velocities up to $\sim$150 km s$^{-1}$.} These redshifts
appear in the rise phase of the flare, then increase rapidly, reach the maximum
in a few minutes, and proceed into the decay phase. Combining the images from
\textit{IRIS} and Atmospheric Imaging Assembly (AIA) on board the {\em Solar
Dynamics Observatory} ({\em SDO}), we propose that the redshifts in the cool
lines are caused by the downflows in the transition region and upper
chromospheric layers, which likely result from a magnetic reconnection leading
to the flare. In addition, the cool \ion{Si}{4} and \ion{C}{2} lines show
gentle redshifts (a few tens of km s$^{-1}$) at some other locations, which
manifest some distinct features from the above locations. This is supposed to
originate from a different physical process.
