Bipolar fuzzy numbers plays a vital role in any Decision-making problem modelled under a bipolar fuzzy environment. In 2018, Akram and Arshad [1] introduced a new ranking function on the class of Trapezoidal Bipolar fuzzy numbers based on the area of the left and right membership function of a TrBFN, and they have discriminated any two TrBFNs by using it. The ranking principle introduced by Akram and Arshad [1] works better only when two bipolar fuzzy numbers have different rankings. We describe that the ranking function does not work with counterexamples when two or more bipolar fuzzy numbers have the same rankings. In this paper, we improve the ranking principle introduced in [1] by introducing a new Improved Score function. Firstly, we discuss the drawbacks and limitations of the ranking function introduced by Akram and Arshad [1]. Secondly, we introduce a new ranking function and study its properties. Thirdly, we introduce a new ranking principle by combining Akram and Arshad’s [1] ranking function and the proposed ranking function. Finally, we show the efficiency of the proposed ranking principle in comparing arbitrary TrBFNs.