Abstract: Transonic problems are solved in nonorthogonal curvilinear coordinate using the stream function equations. To solve the discretization energy and momentum equations simultaneously and iteratively could overcome the problem of unequal density value brought by stream function equation. In this paper a new entropy dissipation method has been put fouard, i. e. without using artificial viscosity dissipation method from J. Von Neumann and R. D. Richtmyer, and only calculating the entropy passed the shock wave, a stable shock wave with one mesh width would be achieved. No matter of how many shock waves in the field, special treatment are not needed. Theoretically speaking, one can obtain the shock wave as narrow as he needs if the enough mesh nodes are taken. It should be pointed out that the methods forwarded in the paper are suitable to any transonic problem, not noly to turbomachinery one.