  We show that for $\alpha \in (2/3, 7/10)$, the log canonical model $\bar
M_4(\alpha)$ of the pair $(\bar M_4, \alpha \delta)$ is isomorphic to the
moduli space $\bar M_4^{hs}$ of h-semistable curves, and that there is a
birational morphism $\Xi: \bar M_4^{hs} \to \bar M_4(2/3)$ that contracts the
locus of curves $C_1\cup_p C_2$ consisting of genus two curves meeting in a
node $p$ such that $p$ is a Weierstrass point of $C_1$ or $C_2$. To obtain this
morphism, we construct a compact moduli space $\bar M_{2,1}^{hs}$ of pointed
genus two curves that have nodes, ordinary cusps and tacnodes as singularity,
and prove that it is isomorphic to Rulla's flip constructed in his thesis.
