  In our recent papers [Sh1,2], we introduced a {\it twisted tensor product} of
dg categories, and provided, in terms of it, {\it a contractible 2-operad
$\mathcal{O}$}, acting on the category of small dg categories, in which the
"natural transformations" are derived. We made use of some homotopy theory
developed in [To] to prove the contractibility of the 2-operad $\mathcal{O}$.
The contractibility is an important issue, in vein of the theory of Batanin
[Ba1,2], according to which an action of a contractible $n$-operad on $C$ makes
$C$ a weak $n$-category.
  In this short note, we provide a new elementary proof of the contractibility
of the 2-operad $\mathcal{O}$. The proof is based on a direct computation, and
is independent from the homotopy theory of dg categories (in particular, it is
independent from [To] and from Theorem 2.4 of [Sh1]).
