  Very sensitive 21cm HI measurements have been made at several locations
around the Local Group galaxy M31 using the Green Bank Telescope (GBT) at an
angular resolution of 9.1', with a 5$\sigma$ detection level of $\rm{N_{HI} =
3.9 \times 10^{17}~cm^{-2}}$ for a 30 $\rm{km~s^{-1}}$ line. Most of the HI in
a 12 square degree area almost equidistant between M31 and M33 is contained in
nine discrete clouds that have a typical size of a few kpc and HI mass of
$10^5$ M$_{\odot}$. Their velocities in the Local Group Standard of Rest lie
between -100 and +40 $\rm{km~s^{-1}}$, comparable to the systemic velocities of
M31 and M33. The clouds appear to be isolated kinematically and spatially from
each other. The total HI mass of all nine clouds is $1.4 \times 10^6$
M$_{\odot}$ for an adopted distance of 800 kpc with perhaps another $0.2 \times
10^6$ M$_{\odot}$ in smaller clouds or more diffuse emission. The HI mass of
each cloud is typically three orders of magnitude less than the dynamical
(virial) mass needed to bind the cloud gravitationally. Although they have the
size and HI mass of dwarf galaxies, the clouds are unlikely to be part of the
satellite system of the Local Group as they lack stars. To the north of M31,
sensitive HI measurements on a coarse grid find emission that may be associated
with an extension of the M31 high-velocity cloud population to projected
distances of $\sim 100$ kpc. An extension of the M31 high-velocity cloud
population at a similar distance to the south, toward M33, is not observed.
