The statement that any phase transition is related to the appearance or disappearance of long-range spatial correlations precludes a finite transition temperature in one-dimensional (1D) systems. In this paper we demonstrate that the 1D Ising model with short-range exchange interactions exhibits a second-order phase transition at a finite temperature relying on the proper choice of the order parameter. To accomplish this, we combined analytical calculations and high-precision entropic sampling simulations and chose a slightly different order parameter, namely the module of the magnetization. Notably, we detected a phase transition with a corresponding critical temperature around 15 K, which is in excellent agreement with experimental results. Our study indicates that an inappropriate choice of the order parameter may mask phase transitions in one-dimensional systems.