  A new type of supersymmetric twistors is proposed and they are called
$\theta$-twistors versus the supertwistors. The $\theta$-twistor is a triple of
spinors including the spinor superspace coordinate $\theta$ instead of the
Grassmannian scalar in the supertwistor triple. The superspace of the
$\theta$-twistors is closed under the superconformal group transformations
except the (super)conformal boosts. Using the $\theta$-twistors in physics
preserves the auxiliary field F in the chiral (0,1/2) supermultiplet contrarily
to the supertwistor description. Moreover, it yields an infinite chain of
higher spin chiral supermultiplets (1/2,1), (1,3/2), (3/2,2),...,(S,S+1/2)
generalizing the scalar massless supermultiplet.
