I will prove some results for the harmonic mean curvature flow in a nonconvex case. It is defined by \frac{dF}{dt} = -\frac{G}{H} u and is a fully nonlinear, weakly parabolic equation, degenerate at the points at which our hypersurface changes its convexity and fast diffusion when H tends to zero. We prove a short time existence of such a flow in a nonconvex case. We also prove that if H does not go to zero, the flow becomes strictly convex at some time and shrinks to a round point.