Abstract: This thesis proposes and discusses a new internal sorting algorithm, which combines mathematics extremum principle with data sorting algorithm. The algorithm expands the concept of minimum, establishes minimum extremum record index and can search very fast record from sequences through indexes of extremum record. As compared with the traditional internal sorting algorithms, the time complexity T(n) of the algorithm is O(n log n) at the most and it's space complexity is O(n). The algorithm guarantees the stability of data sorting while improves the efficiency of sorting.