Consideration is given to the inverse boundary problem of transonic gas dynamics which implies the determination of the channel form according to the distribution of velocity and pressure modulus prescribed on its walls. The system of equations describing plane steady non-rotational gas flow is represented as a two equations symmetrical system which possesses the property of sign definiteness by K. Fridrichs. The suggested differential scheme holds this property. It allows using classical iteration methods for its solution. The examples of numerical calculations are included.