9. If $a \in A$, and $a-1 \notin A, a+1 \notin A$, then $a$ is called an isolated element of set $A$. Therefore, the number of four-element subsets of set $M=\{1,2, \cdots, 9\}$ that have no isolated elements is $\qquad$ .
9.21 .

Consider the smallest element $i$ and the largest element $j$ in a set that satisfies the condition.

Let this set be $A$. Then $i+1 \in A, j-1 \in A$ (otherwise, $i$ or $j$ would be an isolated element).
Thus, $A=\{i, i+1, j-1, j\}$.
And $2 \leqslant i+1<j-1 \leqslant 8$, so the number of ways to choose $i+1, j-1$ is $\mathrm{C}_{7}^{2}=21$. Therefore, the number of four-element subsets of the set $M=\{1,2, \cdots, 9\}$ without isolated elements is 21.