  We introduce new purely twistorial scale-invariant action describing the
composite bosonic D=4 Nambu-Goto string with target space parametrized by the
pair of D=4 twistors. We show that by suitable gauge fixing of local scaling
one gets the bilinear twistorial action and canonical quantization rules for
the two-dimensional twistor-string fields. We consider the Poisson brackets of
all constraints characterizing our model and we obtain four first class
constraints describing two Virasoro constraints and two U(1)xU(1) Kac-Moody
(KM) local phase transformations.
