Abstract: A combined homotopy equation was constructed for solving the generalized linear complementarity problem， which was equivalent to the absolute value equation,  an existence condition of a solution of the generalized linear complementarity problem was obtained based on the homotopy equation,  and this condition was different from that of the usual interval matrix.  An example shows that this condition is not stronger than the regularity condition of the interval, so we obtain a new existence condition of a solution of absolute value equation.

Key words: absolute value equation, homotopy method, column sufficient matrix