To find the square of the radical expression \(-\sqrt{43}\), you can follow these steps:
\[ (-\sqrt{43})^2 \]
When you square a negative number, the negative sign becomes positive:
\[ (-\sqrt{43})^2 = (-1)^2 \cdot (\sqrt{43})^2 = 1 \cdot 43 = 43 \]
Thus, the square of the radical expression \(-\sqrt{43}\) is:
\[ \boxed{43} \]