  We expose the relevance of double occupancy conservation symmetry in
application of the Hubbard-I approach to strongly correlated electron systems.
We propose the utility of a composite method, viz. the Hubbard-I method in
conjunction with strong coupling perturbation expansion, for studying systems
violating the afore--mentioned symmetry. We support this novel approach by
presenting a first successful Hubbard-I type calculation for the description of
the metal-insulator Mott transition in a strongly correlated electron system
with conserved double occupancies, which is a constrained Hubbard Hamiltonian
equivalent to the Hubbard bond charge Hamiltonian with $X=t$. In particular, we
obtain the phase diagram of this system for arbitrary fillings, including
details of the Mott transition at half-filling. We also compare the Hubbard-I
band--splitting Mott transition description with results obtained using the
standard Gutzwiller Approximation (GA), and show that the two approximate
approaches lead to qualitatively different results. In contrast to the GA
applied to the system studied here, the Hubbard-I approach compares favourably
with known exact results for the $d=1$ dimensional chain.
