  Let two Heegaard splittings $V_1 \cup W_1$ and $V_2 \cup W_2$ of a 3-manifold
$M$ be given. We consider the union stabilization $M=V \cup W$ which is a
common stabilization of $V_1 \cup W_1$ and $V_2 \cup W_2$ having the property
that $V=V_1 \cup V_2$. We show that any two Heegaard splittings of a 3-manifold
have a union stabilization. We also give some examples with numerical bounds on
the minimal genus of union stabilization. On the other hand, we give an example
of a candidate for which the minimal genus of union stabilization is strictly
larger than the usual stable genus -- the minimal genus of common
stabilization.
