  We propose a new formulation of the $D=10$ Brink-Schwarz superparticle which
is manifestly invariant under both the target-space super-Poincar\'e group and
the world-line local $N=8$ superconformal group. This twistor-like construction
naturally involves the sphere $S^8$ as a coset space of the $D=10$ Lorentz
group. The action contains only a finite set of auxiliary fields, but they
appear in unusual trilinear combinations. The origin of the on-shell $D=10$
fermionic $\kappa$ symmetry of the standard Brink-Schwarz formulation is
explained. The coupling to a $D=10$ super-Maxwell background requires a new
mechanism, in which the electric charge appears only on shell as an integration
constant.
