  Deep radio observations of the galaxy cluster Abell 781 have been carried out
using the Giant Metrewave Radio Telescope at 325 MHz and have been compared to
previous 610 MHz observations and to archival VLA 1.4 GHz data. The radio
emission from the cluster is dominated by a diffuse source located at the
outskirts of the X-ray emission, which we tentatively classify as a radio
relic. We detected residual diffuse emission at the cluster centre at the level
of S(325 MHz)~15-20 mJy. Our analysis disagrees with Govoni et al. (2011), and
on the basis of simple spectral considerations we do not support their claim of
a radio halo with flux density of 20-30 mJy at 1.4 GHz. Abell 781, a massive
and merging cluster, is an intriguing case. Assuming that the residual emission
is indicative of the presence of a radio halo barely detectable at our
sensitivity level, it could be a very steep spectrum source.
