  We introduce regular series expansion for weakly- and moderately-correlated
fermionic systems, based on Fluctuating Local Field approach. The method relies
on the explicit account of leading fluctuating mode(s) and is therefore
suitable for medium-sized lattices. It can be also used as a solver for the
cluster approximations for infinite-size lattices. We introduce classical
fluctuating field coupled to fermionic collective mode(s). This way,
fluctuations in selected modes are treated in a non-perturbative way. Other
degrees of freedom are accounted for the diagram expansion performed at each
value of the fluctuating field. The method is benchmarked for the $U/t=1$ and
$U/t=2$ Hubbard lattices at half-filling. Results for susceptibility in the
antiferromagnetic channel along with the single particle density of states are
compared with the numerically exact quantum Monte Carlo data. Calculations up
to the third order of the series expansion are performed and show a uniform
convergence to the reference result for the susceptibility. This convergence is
observed well below the DMFT Ne\'el temperature and makes our practically
simple method applicable in a much wider temperature range than DMFT-based
diagrammatic schemes.
