Deformation of Schild string

We attempt to construct new superstring actions with a D-plet of Majorana f ermions psi(A)(B), where B is the D-dimensional space-time index and A is t he two-dimensional spinor index, by deforming the Schild action. As a resul t, we propose three kinds of actions: the first is invariant under N = 1 (t he worldsheet) supersymmetry transformation and the area-preserving diffeom orphism. The second contains the Yukawa type interaction. The last possesse s some nonlocality because of bilinear terms of psi(A)(B). The reasons why completing a Schild type superstring action with psi(A)(B) is difficult are finally discussed.