The problem of on-line scheduling a set of independent jobs on m machines is considered. The goal is to minimize the makespan of the schedule. Graham's List Scheduling heuristic [R. L Graham, SIAM J. Appl. Math., 17(1969), pp. 416-429] guarantees a worst case performance of 2 - 1/m for this problem. This worst case bound cannot be improved for m = 2 and m = 3. For m greater-than-or-equal-to 4, approximation algorithms with worst case performance at most 2 - 1/m - epsilon(m) are presented, where epsilon(m) is some positive real depending only on m.