  In this paper we characterize magnitude-dependent systematics in the proper
motions of the Gaia EDR3 catalog and provide a prescription for their removal.
The reference frame of bright stars (G<13) in EDR3 is known to rotate with
respect to extragalactic objects, but this rotation has proven difficult to
characterize and correct. We employ a sample of binary stars and a sample of
open cluster members to characterize this proper motion bias as a
magnitude-dependent spin of the reference frame. We show that the bias varies
with G magnitude, reaching up to 80 {\mu}as/yr for sources in the range G = 11
- 13, several times the formal EDR3 proper motion uncertainties. We also show
evidence for an additional dependence on the color of the source, with a
magnitude up to 10 {\mu}as/yr. However, a color correction proportional to the
effective wavenumber is unsatisfactory for very red or very blue stars and we
do not recommend its use. We provide a recipe for a magnitude-dependent
correction to align the proper motion of the Gaia EDR3 sources brighter than
G=13 with the International Celestial Reference Frame.
