  Let $\A$ be a unital separable nuclear $C^*$--algebra which belongs to the
bootstrap category $\N$ and $\B$ be a separable stable $C^*$--algebra. In this
paper, we consider the group $\Ext_u(\A,\B)$ consisting of the unitary
equivalence classes of unital extensions $\tau\colon\A\rightarrow Q(\B)$. The
relation between $\Ext_u(\A,\B)$ and $\Ext(\A,\B)$ is established. Using this
relation, we show the half--exactness of $\Ext_u(\cdot,\B)$ and the (UCT) for
$\Ext_u(\A,\B)$. Furthermore, under certain conditions, we obtain the
half--exactness and Bott periodicity of $\Ext_u(\A,\cdot)$.
