the remaining parameters may not be reliably resolved. In previous work (, hereafter the ‘HTPM paper’) we have shown that the inclusion of [Hipparcos]{} data permits us to compute an astrometric solution for all five astrometric parameters of the [Hipparcos]{} stars, based on only one year of [*Gaia*]{} observations. This Hundred Thousand Proper Motions (HTPM, @LL:FM-040) project benefits from the $\sim$24 yr time difference between [Hipparcos]{} and [*Gaia*]{} to improve the proper motions and, for example, detect long-period astrometric binaries. However, a serious limitation of HTPM is that the [Hipparcos]{} stars are not numerous enough to perform an adequate calibration and attitude determination of [*Gaia*]{}. As described in the HTPM paper, additional ‘auxiliary stars’ must therefore be employed. Potentially this could bias the HTPM solution if the [*Gaia*]{} data alone do not allow all five astrometric parameters to be determined for the auxiliary stars.

In the present paper we show that some problems with the HTPM solution can be overcome if the auxiliary stars are replaced by stars from the [*Tycho-2*]{} Catalogue , using their positions at the [Hipparcos]{} epoch to constrain the proper motions.[^1] This allows us to solve the full set of astrometric parameters for the [*Tycho*]{} stars 