This paper introduces a method to enhance an integer linear programming (ILP)-based method for transforming a 1 -order threshold logic gate (1-TLG) to a 2 -order TLG (2-TLG) with lower area cost. We observe that for a 2-TLG, most of the 2 -order weights (2-weights) are zero. That is, in the ILP formulation, most of the variables for the 2-weights could be set to zero. Thus, we first propose three sufficient conditions for transforming a 1-TLG to a 2-TLG by extracting 2-weights. These extracted weights are seen to be more likely non-zero. Then, we simplify the ILP formulation by eliminating the non-extracted 2-weights to speed up the ILP solving. The experimental results show that, to transform a set of 1-TLGs to 2-TLGs, the enhanced method saves an average of 24% CPU time with only an average of 1.87% quality loss in terms of the area cost reduction rate.