  In a previous work, we have constructed a reparametrization invariant
worldsheet action from which one can derive the super-Poincare covariant pure
spinor formalism for the superstring at the fully quantum level. The main idea
was the doubling of the spinor degrees of freedom in the Green-Schwarz
formulation together with the introduction of a new compensating local
fermionic symmetry. In this paper, we extend this "double spinor" formalism to
the case of the supermembrane in 11 dimensions at the classical level. The
basic scheme works in parallel with the string case and we are able to
construct the closed algebra of first class constraints which governs the
entire dynamics of the system. A notable difference from the string case is
that this algebra is first order reducible and the associated BRST operator
must be constructed accordingly. The remaining problems which need to be solved
for the quantization will also be discussed.
