  This paper is devoted to studying the following nonlinear biharmonic
Schr\"odinger equation with combined power-type nonlinearities
\begin{equation*} \begin{aligned}
  \Delta^{2}u-\lambda u=\mu|u|^{q-2}u+|u|^{4^*-2}u\quad\mathrm{in}\
\mathbb{R}^{N}, \end{aligned} \end{equation*} where $N\geq5$, $\mu>0$,
$2<q<2+\frac{8}{N}$, $4^*=\frac{2N}{N-4}$ is the $H^2$-critical Sobolev
exponent, and $\lambda$ appears as a Lagrange multiplier. By analyzing the
behavior of the ground state energy with respect to the prescribed mass, we
establish the existence of normalized ground state solutions. Furthermore, all
ground states are proved to be local minima of the associated energy
functional.
