  {We report our observations of a swirling flare-related EUV jet on 2011
October 15.} {We utilised the EUV observations from SDO/AIA. We extracted a
wide slit along the jet axis and 12 thin slits across its axis to investigate
the longitudinal motion and transverse rotation. We also used data from
STEREO/EUVI to investigate the 3D structure of the jet. Gound-based H$\alpha$
images provide a good opportunity to explore the relationship between the cool
surge and hot jet. LOS magnetograms from SDO/HMI enable us to study the
magnetic evolution of the flare/jet event.} {The onset of jet eruption
coincided with the start time of C1.6 flare impulsive phase. The initial
velocity and acceleration of the longitudinal motion were 254$\pm10$ km
s$^{-1}$ and $-97\pm5$ m s$^{-2}$, respectively. The jet presented helical
structure and transverse swirling motion at the beginning of its eruption. The
counter-clockwise rotation slowed down from an average velocity of $\sim$122 km
s$^{-1}$ to $\sim$80 km s$^{-1}$. The interwinding thick threads of the jet
untwisted into multiple thin threads during the rotation that lasted for 1
cycle with a period of $\sim$7 min and an amplitude that increases from
$\sim$3.2 Mm at the bottom to $\sim$11 Mm at the upper part. Afterwards, the
curtain-like leading edge of the jet continued rising without rotation, leaving
a dimming region behind before falling back to the solar surface. The
appearance/disappearance of dimming corresponded to the longitudinal
ascending/descending motions of jet. Cospatial H$\alpha$ surge and EUV dimming
imply that the dimming resulted from the absorption of hot EUV emission by cool
surge. The flare/jet event was caused by continuous magnetic cancellation
before the start of flare. The jet was associated with the open magnetic fields
at the edge of AR 11314.}
