Algorithm for listing permutations for n elements is an arduous task. This paper attempts to introduce a novel method for generating permutations. The fundamental concept for this method is to seek a starter set to begin with as an initial set to generate all distinct permutations. In order to demonstrate the algorithm, we are keen to list the permutations with the special references for cases of three and four objects. Based on this algorithm, a new method for listing permutations is developed and analyzed. This new permutation method will be compared with the existing lexicographic method. The results revealed that this new method is more efficient in terms of computation time.