  Starting with the first-order formulation of the massless superparticle model
on the $AdS_5\times S^5$ superbackground and presenting the momentum components
tangent to $AdS_5$ and $S^5$ subspaces as bilinear combinations of the
constrained $SU(2)$-Majorana spinors allows to bring the superparticle's
Lagrangian to the form quadratic in supertwistors. The $SU(2,2|4)$
supertwistors are assembled into a pair of $SU(2)$ doublets, one of which has
even $SU(2,2)$ and odd $SU(4)$ components, while the other has odd $SU(2,2)$
and even $SU(4)$ components. They are subject to the first-class constraints
that generate the $psu(2|2)\oplus u(1)$ gauge algebra. This justifies
previously proposed group-theoretic definition of the $AdS_5\times S^5$
supertwistors and allows to derive the incidence relations with the $(10|32)$
supercoordinates of the $AdS_5\times S^5$ superspace. Whenever superparticle
moves within the $AdS_5$ subspace of the $AdS_5\times S^5$ space-time, twistor
formulation of its Lagrangian involves just one $SU(2)$ doublet of $SU(2,2|4)$
supertwistors with even $SU(2,2)$ and odd $SU(4)$ components. If in addition
particle's 5-momentum is null, four first-class constraints which are the
$su(2)\oplus u(1)$ generators single out upon quantization the states of $D=5$
$N=8$ gauged supergravity multiplet in the superambitwistor formulation.
