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In this paper we characterize magnitude-dependent systematics in the propermotions 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 withrespect to extragalactic objects, but this rotation has proven difficult tocharacterize and correct. We employ a sample of binary stars and a sample ofopen cluster members to characterize this proper motion bias as amagnitude-dependent spin of the reference frame. We show that the bias varieswith 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 showevidence for an additional dependence on the color of the source, with amagnitude up to 10 {\mu}as/yr. However, a color correction proportional to theeffective wavenumber is unsatisfactory for very red or very blue stars and wedo not recommend its use. We provide a recipe for a magnitude-dependentcorrection to align the proper motion of the Gaia EDR3 sources brighter thanG=13 with the International Celestial Reference Frame.

Characterizing and correcting the proper motion bias of the bright Gaia EDR3 sources