  To exhibit the possible origin of the inner complexity of the Berkovits's
pure spinor approach, we consider the covariant BRST quantization of the D=11
massless superparticle (M0-brane) in its spinor moving frame or twistor-like
Lorentz harmonics formulation. The presence of additional twistor-like
variables (spinor harmonics) allows us to separate covariantly the first and
the second class constraints. After taking into account the second class
constraints by means of Dirac brackets and after further reducing the first
class constraints algebra, the dynamical system is described by the cohomology
of a simple BRST charge associated to the d=1, n=16 supersymmetry algebra. The
calculation of the cohomology of this BRST operator requires a regularization
which implies the complexification of the bosonic ghost associated to the
kappa-symmetry and further leads to a complex (non-Hermitian) BRST charge which
is essentially the `pure spinor' BRST operator by Berkovits, but with a
composite pure spinor.
