The quantization of the superstring with N = 1 global supersymmetry is considered in the functional integral formalism. The term in the effective action defined by the conformal anomaly is calculated. It is shown that the effective action is determined not only by the intrinsic properties of the surface (i.e. by the metric hαβ) but depends also on the way the surface is embedded in D-dimensional space (i.e. on the second quadratic form of the surface). The selfduality of N = 1 superstring theory with a Wess-Zumino term is pointed out.