For two Banach algebras $\cal A$ and $\cal B$, an important and interesting product ${\cal A} \times_{\theta}{\cal B}$, called $\theta$-Lau product, was recently introduced and studied for some nonzero characters $\theta$ on $\cal B$. Here, we characterize the notion of essential contractibilitybetween $\cal A$ and $\cal B$ and their $\theta$-Lau product.
