For the generalized linear complementarity problems
where , , is an positive semi-definite matrix and , the author presents a globally convergent projection and contraction method which is a modification of his earlier method [Appl. Math. Optimization 25, No. 3, 247-262 (1992; Zbl 0767.90086)]. He describes the new algorithm and its relation to the original one. The convergence properties of the new algorithm and some numerical results are given.