  We attempt to construct new superstring actions with a $D$-plet of Majorana
fermions $\psi^{\cal B}_A$, where ${\cal B}$ is the $D$ dimensional space-time
index and $A$ is the two dimensional spinor index, by deforming the Schild
action. As a result, we propose three kinds of actions: the first is invariant
under N=1 (the world-sheet) supersymmetry transformation and the
area-preserving diffeomorphism. The second contains the Yukawa type
interaction. The last possesses some non-locality because of bilinear terms of
$\psi^{\cal B}_A$. The reasons why completing a Schild type superstring action
with $\psi^{\cal B}_A$ is difficult are finally discussed.
