We propose a new formulation of the D = 11 supermembrane theory that i
nvolves commuting spinors (twistor-like variables) and exhibits a mani
fest n-extended world-volume supersymmetry (3 less-than-or-equal-to n
less-than-or-equal-to 8). This supersymmetry replaces n components of
the usual kappa-symmetry. We argument that, at least for n = 8, this f
ormulation is classically equivalent to the standard one.