In the present paper some points concerning transonic flows and traditional potential method are briefly reviewed. Improved potential formulations in which the shortcomings of the isentropic potential function are overcome have been discussed andcompared systematically. The analysis of the compatibility of isentropy and irrotationality conditions shows that the former one is not the necessary presumption of the latter one. The affection of the artificial density supposition on the Rankin-Hugoniot relation is also discussed. The purpose of this paper is to present more universal theoretical basis and offer approaches for improving the accuracy of shock wave computation and thus to extend the application range of potential function methods in transonic flows.