We study the existence and orbital stability of normalized solutions of the biharmonic equation with the mixed dispersion and a general nonlinear term

$$\gamma {\mathrm{\Delta }}^{2}u-\beta \mathrm{\Delta }u+\lambda u=f(u),x\in {\mathbb{R}}^N$$

with a priori prescribed $L^2$-norm constraint $S_a:=\left\{u\in H^2({\mathbb{R}}^N):{\int }_{{\mathbb{R}}^N}|u{|}^{2}dx=a\right\},$ where $a>0$, $\gamma >0,\beta \in \mathbb{R}$ and the nonlinear term $f$ satisfies the suitable $L^2$-subcritical assumptions. When $\beta \ge 0$, we prove that there exists a threshold value $a_0\ge 0$ such that the equation above has a ground state solution which is orbitally stable if $a>a_0$ and has no ground state solution if $a<a_0$. However, for $\beta <0$, this case is more involved. Under an additional assumption on $f$, we get the similar results on the existence and orbital stability of ground state. Finally, we consider a specific nonlinearity $f(u)=|u{|}^{p-2}u+\mu |u{|}^{q-2}u,2<q<p<2+8/N,\mu <0$ under the case $\beta <0$, which does not satisfy the additional assumption. And we use the example to show that the energy in the case $\beta <0$ exhibits a more complicated nature than that of the case $\beta \ge 0$.