  High accuracy proper motions (PMs) of M31 and other Local Group satellites
have now been provided by the {\it Gaia} satellite. We revisit the Timing
Argument to compute the total mass $M$ of the Local Group from the orbit of the
Milky Way and M31, allowing for the Cosmological Constant. We rectify for a
systematic effect caused by the presence of the Large Magellanic Cloud (LMC).
The interaction of the LMC with the Milky Way induces a motion towards the LMC.
This contribution to the measured velocity of approach of the Milky Way and M31
must be removed. We allow for cosmic bias and scatter by extracting correction
factors tailored to the accretion history of the Local Group. The distribution
of correction factors is centered around $0.63$ with a scatter $\pm 0.2$,
indicating that the Timing Argument significantly overestimates the true mass.
Adjusting for all these effects, the estimated mass of the Local Group is $ M =
3.4^{+1.4}_{-1.1} \times 10^{12} M_{\odot}$ (68 % CL) when using the M31
tangential velocity $ 82^{+38}_{-35}$ km/s. Lower tangential velocity models
with $59^{+42}_{-38}$ km/s (derived from the same PM data with a flat prior on
the tangential velocity) lead to an estimated mass of $ M = 3.1^{+1.3}_{-1.0}
\times 10^{12} M_{\odot}$ (68 % CL). By making an inventory of the total mass
associated with the 4 most substantial LG members (the Milky Way, M31, M33 and
the LMC), we estimate the known mass is in the range $3.7^{+0.5}_{-0.5} \times
10^{12} \, M_{\odot}$.
