  We provide a linearised superfield description of the exotic non-metric
$N=(4,0)$ supergravity in $D=6$, by using a pure spinor superfield formalism.
The basic field $\Psi$ is a ghost number 2 scalar, transforming in the same
R-symmetry module as the tensor fields. Partial results for the $N=(3,1)$ model
are presented.
