Many optimal uniprocessor schedulers, such as Earliest Deadline First (EDF) and Rate Monotonic (RM), do not have a good schedulability bound on multiprocessor systems. In this paper, we study an on-line algorithm Earliest Deadline First until Zero laxity (EDZL) for multiprocessor systems. A set of tasks scheduled by EDZL is scheduled using EDF until a job experiences a zero laxity. To avoid the job from missing its deadline, the priority of the job is immediately promoted to the highest priority. We derive the schedulability bound of 3/2+|u max-1/2| for two-processor systems, where u max is the maximum utilization of an individual task in the given task set. We also discuss the best known upper bound and lower bound on EDZL schedulability conditions.