Abstract: We used the homotopy method to solve the linear complementarity problem. By constructing a new homotopy equation for the linear complementarity problem corresponding to the R₀matrix, we gave a new condition for the existence of homotopy path. Under this condition, we proved the boundedness and convergence of the homotopy path, and obtained a condition for the existence of a solution of the linear complementarity problem.

Key words: linear complementarity problem, homotopy method, R₀matrix