We describe a diagonal condition on the Khovanov complex of tangles, show
that this condition is satisfied by the Khovanov complex of the single crossing
tangles, and prove that it is preserved by alternating planar algebra
compositions. Hence, this condition is satisfied by the Khovanov complex of all
alternating tangles. Finally, in the case of 0-tangles, that is links, our
condition is equivalent to a well known result which states that the Khovanov
homology of a non-split alternating link is supported in two lines.