The exact response time analysis for fixed priority scheduling (FPS) in the lowest priority first-based feasibility tests is commonly required as a part of system design tools. This letter proposes an efficient method for this, which we named incremental lower bound (ILB) calculation method. Compared to the best algorithm that has been known so far, which is the incremental calculation method, ILB reduces the feasibility test iterations/run times by more than 38% and 20% regardless of varying utilization and the number of tasks in task sets.