An old puzzle of theoretical molecular spectroscopy, the derivation of the internal axis system (IAS) of molecules with one large amplitude internal motion and asymmetric top and asymmetric frame has been solved by a simple and transparent method. The basic idea has been to consider the large-amplitude-coordinate-dependent IAS as the result of quantum mechanical evolution in rho of an initial system of axes, where rho denotes the coordinate describing the large amplitude motion. A special choice of the operator governing rho evolution guarantees that the rho evolved system is the IAS. Floquet theory provides both a simple analytical expression for the evolution-matrix and a means to efficiently calculate this matrix. Numerical examples have revealed fast convergence of the method to the IAS.