To estimate plait points of ternary liquid-liquid equilibria(LLE) of type 1, a novel method is proposed. In general, the plait points resulting from correlation of the tie lines with the thermodynamic models are not located on the experimentally determined binodal curves. In addition, determination of the plait points using the correlation methods requires binodal curve data as well as the tie line data. In the proposed method, two parameters, weight fraction of a component and the ratio of weight fractions of remaining two components, are varied until linearity between logarithmic tie-line length and logarithmic distance of the tie-line from the plait point is attained so that the order parameter equation of Widom is satisfied. With this method, plait points of several ternary systems are estimated and it turns out that the results are favorably comparable with the results obtained by the method proposed by Treybal et al. However, it needs to emphasize that the method proposed in this paper uses only tie-line data while the method of Treybal et al. with the correlation of Othmer and Tobias requires experimental binodal curve data in addition to the tie-line data.