In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface

under the Gauss curvature flow. Let

be the embeddings of the sphere in

such that

is the surface at time t and

. As a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate on the interface separating the nonconvex part from the strictly convex side, since one of the curvature will be zero on the interface. By expressing the strictly convex part of the surface near the interface as a graph of a function

and the non-convex part of the surface near the interface as a graph of a function

, we show that if at time

,

vanishes linearly at the interface, the

will become smooth up to the interface for long time before focusing.