  We present a new coalignment method for the EUV Imaging Spectrometer (EIS) on
board the Hinode spacecraft. In addition to the pointing offset and spacecraft
jitter, this method determines the roll angle of the instrument, which has
never been systematically measured, and is therefore usually not corrected. The
optimal pointing for EIS is computed by maximizing the cross-correlations of
the Fe XII 195.119 \r{A} line with images from the 193 \r{A} band of the
Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory
(SDO). By coaligning 3336 rasters with high signal-to-noise ratio, we estimate
the rotation angle between EIS and AIA and explore the distribution of its
values. We report an average value of (-0.387 $\pm$ 0.007)\deg. We also provide
a software implementation of this method that can be used to coalign any EIS
raster.
