The general S matrix of nuclear reaction is derived by the method of second quantization in order to take account of antisymmetrization of the total system. As an example of the general theory, a deuteron stripping reaction is treated. The amplidue obtained by this method is compared with those obtained by other theories in this reaction. The amplitude of this reaction is discussed for a special target which seems to demonstrate the effect of antisymmetrization most clearly. In the case of O17(d,p)O18 the effect of antisymmetrization becomes comparable with the direct part.