Fatigue cracking is one of the crucial distresses considered for the design of flexible pavements. The initiation of fatigue cracking occurs in the binder phase of an asphalt mixture. The linear amplitude sweep (LAS) test was developed to analyze the fatigue damage in the asphalt binder. AASHTO T391 provides a method to analyze the LAS test data by fitting a power equation between the fatigue parameter (G*sinδ) and damage intensity. This method has some inherent weaknesses of overfitting or underfitting of the data at different damage levels. This study proposes a new method where a total curve is divided into two parts that fit the data in two different equations and then sum them up. The first part comprises of the data up to cumulative damage corresponding to the maximum effective stress, and the second part consists of accumulated damage in the material till it reaches the maximum strain (30 %). This method is called the bifurcation method in this paper. LAS test data of 27 long-term aged bitumen samples having different physical properties is used to determine the number of fatigue life cycles (Nf) by these two methods, and results are compared in terms of mean absolute percentage error (MAPE), root mean square error (RMSE), and residual sum of squares (RSS). It is shown that there is a significant reduction in the errors when the data fitting was done using the proposed bifurcation method. Further, the ranking was allotted to the samples based on the number of fatigue life cycles (Nf) at three different strain levels (2.5 %, 5 %, and 10 %) at intermediate-temperature conditions estimated using two methods. The shift indicator parameter was used to analyze the variability in the ranking of the samples due to changes in the strain levels. The study concludes that the proposed bifurcation method fits the predicted values more accurately than the prescribed power law.