  We present an alternative scheme to the widely used method of representing
the basis of one-band Hubbard model through the relation
$I=I_{\uparrow}+2^{M}I_{\downarrow}$ given by H. Q. Lin and J. E. Gubernatis
[Comput. Phys. 7, 400 (1993)], where $I_{\uparrow}$, $I_{\downarrow}$ and $I$
are the integer equivalents of binary representations of occupation patterns of
spin up, spin down and both spin up and spin down electrons respectively, with
$M$ being the number of sites. We compute and store only $I_{\uparrow}$ or
$I_{\downarrow}$ at a time to generate the full Hamiltonian matrix. The
non-diagonal part of the Hamiltonian matrix given as
${\cal{I}}_{\downarrow}\otimes{\bf{H}_{\uparrow}} \oplus
{\bf{H}_{\downarrow}}\otimes{\cal{I}}_{\uparrow}$ is generated using a
bottom-up approach by computing the small matrices ${\bf{H}_{\uparrow}}$(spin
up hopping Hamiltonian) and ${\bf{H}_{\downarrow}}$(spin down hopping
Hamiltonian) and then forming the tensor product with respective identity
matrices ${\cal{I}}_{\downarrow}$ and ${\cal{I}}_{\uparrow}$, thereby saving
significant computation time and memory. We find that the total CPU time to
generate the non-diagonal part of the Hamiltonian matrix using the new one spin
configuration basis scheme is reduced by about an order of magnitude as
compared to the two spin configuration basis scheme. The present scheme is
shown to be inherently parallelizable. Its application to translationally
invariant systems, computation of Green's functions and in impurity solver part
of DMFT procedure is discussed and its extention to other models is also
pointed out.
