  An improved weighting algorithm applied to hadron showers has been developed
for a fine grained LAr calorimeter. The new method uses tabulated weights which
depend on the density of energy deposited in individual cells and in a
surrounding cone whose symmetry axis connects the interaction vertex with the
highest energy cluster in the shower induced by a hadron. The weighting of the
visible energy and the correction for losses due to noise cuts are applied in
separate steps. In contrast to standard weighting procedures the new algorithm
allows to reconstruct the total energy as well as the spatial energy deposition
on the level of individual calorimeter cells. The linearity and the energy
resolution of the pion signal in the momentum interval 2 GeV/c <= p <= 20 GeV/c
studied in this analysis are considerably improved in comparison to the
standard weighting algorithm as practiced presently by the H1 collaboration.
Moreover the energy spectra reconstructed with the new method follow in a broad
interval a Gaussian distribution and have less pronounced tails.
