We attempt to construct new superstring actions with a D-plet of Majorana fermions [Formula: see text], where 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 worldsheet) supersymmetry transformation and the area-preserving diffeomorphism. The second contains the Yukawa type interaction. The last possesses some nonlocality because of bilinear terms of [Formula: see text]. The reasons why completing a Schild type superstring action with [Formula: see text] is difficult are finally discussed.