This paper presents a new Lagrangian approach to the numeric solution of the equation of gas dynamics in two dimensions. This, the signal method, is implemented here as a free Lagrange method in the code FLAME. The signal method is conservative, stable, unsplit, positive definite, accurately tracks strong shock fronts with ease, and adapts to and follows complex gas flows for long times. No artificial viscosities are introduced. No special knowledge of the solution is required in advance and only local information is used.