  We calculate the exact analytical coefficients of the $\beta$ expansion of
the grand-canonical partition function of the unidimensional Hubbard model up
to order $\beta^5$, using an alternative method, based on properties of the
Grassmann algebra. The results derived are non-perturbative and no restrictions
on the set of parameters that characterize the model are required. By applying
this method we obtain analytical results for the thermodynamical quantities, in
the high-temeprature limit, for arbitrary density of electrons in the
unidimensional chain.
