Finding block triangular matrix similar to "almost symmetric" block matrix

Question

I have a block matrix $$M=\begin{bmatrix}A & B \\ -B & 0\end{bmatrix}$$ where $A$ is negative definite ($A \prec 0$) and $B$ is positive semidefinite ($B \succeq 0$). It might not matter, but $A$ and $B$ share the same dimension. I want to find a similarity transformation that can turn this into a block triangular matrix. As you can see, this block matrix is sort of a "reverse" block triangle matrix. I was wondering if someone might have a "trick" to find such a similarity transformation.