  We consider the decoding of LDPC codes over GF(q) with the low-complexity
majority algorithm from [1]. A modification of this algorithm with multiple
thresholds is suggested. A lower estimate on the decoding radius realized by
the new algorithm is derived. The estimate is shown to be better than the
estimate for a single threshold majority decoder. At the same time the
transition to multiple thresholds does not affect the order of complexity.
