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The index portfolio model attempts to form a portfolio whose time series in the market can trace the selected index as much as possible. The traditional index portfolio model, estimated coefficients models proposed by Salkin, established the portfolio by minimizing the square tracking error. In this paper, a novel index portfolio model formed by minimizing the absolute tracking error is proposed. In addition to preserving the characteristics of Salkin’s model, the proposed model can guarantee obtaining the global optimum solution and, in contrast to Salkin’s model, it can avoid the effect of the extreme value, which Salkin’s model may not. Also in contrast to the traditional model, the proposed one is a linear programming model and can then include practical constraints in the models, including the transaction cost constraints and limited stock catalog constraints. How the improved models address these constraints would be discussed as well. Moreover, different empirical studies in the Taiwan Stock Market are provided to demonstrate the proposed model’s effectiveness