A method for the free network adjustment is proposed, based on the application of generalized inverse matrix (g-inverse). If the network adjustment is executed according to the solution with parameters, especially when all coordinates are considered as parameters to keep unity strength, the matrix of normal equation will be singular. This paper discusses the problem of singular matrix and the analysis of accuracy between conventional method and the free network adjustment of trilateration. In case of the adjustment, the RMS errors of adjusted X, Y coordinates are increased to 35.6% in a polygon, central-point figure, and 50.5% in a quadrilateral. In the elements of error ellipse, the RMS errors are decreased by $pm$24.5% (a) and $pm$5.0 % (b) in the polygon, $pm$42.6% (a) and $pm$49.2% (b) in the quadrilateral. Introduction of free network adjustment, therefore, could be applied to improvement of relative accuracy in the horizontal positioning.