  Using an N=4, d=1 superfield approach, we construct an N=8 supersymmetric
action of the self-interacting off-shell N=8 multiplet {\bf (1, 8, 7)}. This
action is found to be invariant under the exceptional N=8, d=1 superconformal
group F(4) with the R-symmetry subgroup SO(7). The general N=8 supersymmetric
{\bf (1, 8, 7)} action is a sum of the superconformal action and the previously
known free bilinear action. We show that the general action is also
superconformal, but with respect to redefined superfield transformation laws.
The scalar potential can be generated by two Fayet-Iliopoulos N=4 superfield
terms which preserve N=8 supersymmetry but break the superconformal and SO(7)
symmetries.
