This paper proposes one Levy-based, Randomized Insertion-Based Trigonometric Algorithm (RITA) that uses the insertion strategy used by Nawaz, Enscore and Ham (NEH) algorithm. It is a two-phase heuristic for solving permutation flow shop scheduling problems (PFSSP) for the makespan criterion. Since the algorithm consists of two phases, there are two function evaluations per iteration. NEH sequence and makespan are used as the seed in the initialization stage. In phase-I, first two jobs are taken as the initial partial sequence and in phase-II, two jobs are randomly selected as the initial partial sequence. Insertion strategy is implemented in both the phases. Benchmark datasets proposed by Taillard, Vallada (Small), Carlier, Demirkol, Reeves and Heller totaling 401 in numbers are used to analyze the performance of the new algorithm. The results are compared with those of NEH for each dataset. The simulations show that the new algorithm yields better results than NEH but, at the cost of computation time.