  Let $\bfT$ is a certain tensor product of simple dyadic shifts defined below.
We prove here that for dyadic bi-parameter commutator the following equivalence
holds $ \|\bfT b-b \bfT \| \asymp \|b\|_{bmo^d}$. This result is well-known for
many types of bi-parameter commutators, see \cite{FS}, \cite{DLWY} and
\cite{DPSK} for more details.
