  We present a novel approach for a systematic large--spin expansion of the
$t$-$J$ Hamiltonian which enables us to work without the constraint of no
double occupancy. In our scheme we can perform the large--spin limit ensuring
that the low energy spin excitations are in {\em exact} correspondence with the
physical excitations of the $s={1\over2}$ Hilbert space. As a consequence, we
expect a smooth dependence of the physical quantities on the expansion
parameter $1/ s$. As a first application of the method we study the case of a
single hole in a N\'eel background. A systematic expansion in fluctuations
about this stable solution indicates that by increasing $t/J$ the quasiparticle
weight strongly depends on the momentum carried by the hole. Results, obtained
on small lattice sizes, are found in excellent agreement with exact
diagonalization data.
