Although the stellar halo accounts for just ∼1% of the total stellar mass of the Milky Way, the kinematics of halo stars can tell us a lot about the origins and evolution of our Galaxy. It has been shown that the high transverse velocity stars in Gaia DR2 reveal a double sequence in the Hertzsprung-Russell (HR) diagram, indicating a duality in the local halo within 1 kpc. We fit these stars by updating the popular Besançon/Galaxia model, incorporating the latest observational results for the stellar halo. We are able to obtain a good match to the Gaia data and provide new constraints on the properties of the disc and halo. In particular, we show that the thick disc contribution to this high velocity tail is small, but not negligible, and likely has an influence on the red sequence of the HR diagram.