  In this article, we study the existence of normalized ground state solutions
for the following biharmonic nonlinear Schr\"{o}dinger equation with combined
nonlinearities \begin{equation*}
  \Delta^2u=\lambda u+\mu|u|^{q-2}u+|u|^{p-2}u,\quad \text {in $\mathbb{R}^N$}
\end{equation*} having prescribed mass \begin{equation*}
  \int_{\mathbb{R}^N}|u|^2dx=a^2, \end{equation*} where $N\geq2$, $\mu\in
\mathbb{R}$, $a>0$, $2<q<p<\infty$ if $2\leq N\leq 4$, $2<q<p\leq 4^*$ if
$N\geq 5$, and $4^*=\frac{2N}{N-4}$ is the Sobolev critical exponent and
$\lambda\in \mathbb{R}$ appears as a Lagrange multiplier. By using the Sobolev
subcritical approximation method, we prove the second critical point of
mountain pass type for the case $N\geq5$, $\mu>0$, $p=4^*$, and
$2<q<2+\frac{8}{N}$. Moreover, we also consider the case $\mu=0$ and $\mu<0$.
