  In this paper we present a new parsing algorithm for linear indexed grammars
(LIGs) in the same spirit as the one described in (Vijay-Shanker and Weir,
1993) for tree adjoining grammars. For a LIG $L$ and an input string $x$ of
length $n$, we build a non ambiguous context-free grammar whose sentences are
all (and exclusively) valid derivation sequences in $L$ which lead to $x$. We
show that this grammar can be built in ${\cal O}(n^6)$ time and that individual
parses can be extracted in linear time with the size of the extracted parse
tree. Though this ${\cal O}(n^6)$ upper bound does not improve over previous
results, the average case behaves much better. Moreover, practical parsing
times can be decreased by some statically performed computations.
