Let $n \geq 3$. Take an $2n \times 2n$ chessboard, and remove $2$ white pieces and $2$ black pieces, can you always cover it with dominoes?

Question

I am reading "Kombinatorika" by Laszlo Lovasz, Katalin Vesztergombi and Jozsef Pelikan(in Japanese, translated and arranged by Jin Akiyama and Peter Frankl).

There is the following problem in this book:

Let $n \geq 3$. Take an $2n \times 2n$ chessboard, and remove $2$ white pieces and $2$ black pieces, can you always cover it with dominoes?

The authors(or the translators) wrote "No. But we don't write an example.".

I wonder why the authors(or the translators) didn't write an example since there is an obvious example(see the image below):

By the way, I checked the case $n = 3,4,5$ by my Java program (which uses bipartite matching algorithm) and I was not able to find a non-trivial example.
Is there non-trivial examples?