  We show that there is an associative algebra $\widetilde{H}_n$ such that,
over a base ring $R$ of characteristic 2, Khovanov's arc algebra $H_n$ is
isomorphic to the algebra $\widetilde{H}_n[x]/(x^2)$. We also show a similar
result for bimodules associated to planar tangles and prove that there is no
such isomorphism over $\mathbb{Z}$.
