4. Let $a$ be a real number. If there exists a real number $t$, such that $\frac{a-\mathrm{i}}{t-\mathrm{i}}+\mathrm{i}$ is a real number (where $\mathrm{i}$ is the imaginary unit), then the range of values for $a$ is . $\qquad$
$$
\begin{array}{l}
\frac{a-\mathrm{i}}{t-\mathrm{i}}+\mathrm{i}=\frac{a+\mathrm{i}}{t+\mathrm{i}}-\mathrm{i} \Rightarrow \frac{a+\mathrm{i}}{t+\mathrm{i}}-\frac{a-\mathrm{i}}{t-\mathrm{i}}=\frac{(a+\mathrm{i})(t-\mathrm{i})-(a-\mathrm{i})(t+\mathrm{i})}{t^{2}+1}=2 \mathrm{i} \\
\Rightarrow t-a=t^{2}+1 \Rightarrow -a=t^{2}-t+1=\left(t-\frac{1}{2}\right)^{2}+\frac{3}{4} \geqslant \frac{3}{4},
\end{array}
$$

Therefore, the range of values for $a$ is $\left(-\infty,-\frac{3}{4}\right]$.