  We show that a two twistor phase space {\`a} priori describing two non
localized massless and spinning particles may be decomposed into a product of
three independent phase spaces: the (forward) cotangent bundle of the Minkowski
space, the cotangent bundle to a circle (electric charge phase space) and the
cotangent bundle to the real projective spinor space. Reduction of this 16
dimensional phase space with respect to two mutually commuting conformal
scalars (the electric charge and the difference between the two helicities)
produces a 12 dimensional extended relativistic phase space\cite{zak}
describing a massive spinning particle.
