4. Let $t \in \mathbf{R},(t+1)(1-|t|)>0$ holds if and only if ( ).
A. $|t|-1$ and $t \neq 1$
C. $t<1$ and $t \neq-1$
D. $t \neq \pm 1$
4. C. From the problem, we get $\left\{\begin{array}{l}t+1>0 \\ 1-|t|>0\end{array}\right.$ or $\left\{\begin{array}{l}t+1<0 \\ 1-|t|<0\end{array}\right.$. Therefore, $t \in(-\infty,-1) \cup(-1,1)$.