  The stability of the insulating regime of the Hubbard model on a
$d$-dimensional lattice, which is characterized by an exponential decay of the
Green's functions, is investigated in terms of a cluster expansion. This
expansion for the Green's function is organized in terms of connected clustered
transfer matrices. An upper bound for the expansion terms is derived for the
hopping rate ${\bar t}$ depending on the coupling constant $U$ as ${\bar
t}<U/4d$. This implies an upper bound for the decay length of the Green's
function.
