Context : The properties of solar flare plasma can be determined from the observation of optically thin lines .
The emitting ion distribution determines the shape of the spectral line profile , with an isothermal Maxwellian ion distribution producing a Gaussian profile .
Non-Gaussian line profiles may indicate more complex ion distributions .

Aims : We investigate the possibility of determining flare-accelerated non-thermal ion and/or plasma velocity distributions .

Methods : We study EUV spectral lines produced during a flare SOL2013-05-15T01:45 using the Hinode EUV Imaging Spectrometer ( EIS ) .
The flare is located close to the eastern solar limb with an extended loop structure , allowing the different flare features : ribbons , hard X-ray ( HXR ) footpoints and the loop-top source to be clearly observed in UV , EUV and X-rays .
EUV line spectroscopy is performed in seven different regions covering the flare .
We study the line profiles of the isolated and unblended Fe XVI lines ( \lambda 262.9760 ~ { } Å ) mainly formed at temperatures of \sim 2 to 4 MK .
Suitable Fe XVI line profiles at one time close to the peak soft X-ray emission and free of directed mass motions are examined using : 1. a higher moments analysis , 2 .
Gaussian fitting , and 3. by fitting a kappa distribution line profile convolved with a Gaussian to account for the EIS instrumental profile .

Results : Fe XVI line profiles in the flaring loop-top , HXR footpoint and ribbon regions can be confidently fitted with a kappa line profile with an extra variable \kappa , giving low , non-thermal \kappa values between 2 and 3.3 .
An independent higher moments analysis also finds that many of the spectral line kurtosis values are higher than the Gaussian value of 3 , even with the presence of a broad Gaussian instrumental profile .

Conclusions : A flare-accelerated non-thermal ion population could account for both the observed non-Gaussian line profiles , and for the Fe XVI ‘ excess ’ broadening found from Gaussian fitting , if the emitting ions are interacting with a thermalised \sim 4 MK electron population , and the instrumental profile is well-approximated by a Gaussian profile .