  It is shown that every $n$-vertex graph that admits a 2-bend RAC drawing in
the plane, where the edges are polylines with two bends per edge and any pair
of edges can only cross at a right angle, has at most $20n-24$ edges for $n\geq
3$. This improves upon the previous upper bound of $74.2n$; this is the first
improvement in more than 12 years. A crucial ingredient of the proof is an
upper bound on the size of plane multigraphs with polyline edges in which the
first and last segments are either parallel or orthogonal.
