Passive optical network (PON) is a highly dynamic access network that effectively converge several service providers. In a time cycle, some optical network units (ONUs) of PON may miss the usual polling instant called unstable ONUs. According to the existing early dynamic bandwidth allocation (E-DBA) algorithm, once an ONU miss the usual polling instant it needs to be waited until the end of transmissions from the entire stable ONUs. So the unstable ONUs suffers from more waiting time than the stable ONUs. This paper proposes a new DBA algorithm called modified E-DBA (ME-DBA) algorithm, for reduction of waiting times of the unstable ONUs. In the proposed algorithm, total ONUs are divided into several small groups. The data packets from all the stable ONUs of a group are transmitted 1st and then the data packets from the unstable ONUs of that group are transmitted. We have analyzed and compared the performance of the proposed ME-DBA algorithm with the existing E-DBA algorithm in terms of the delay and waiting time of the unstable ONUs by simulations. The simulation results show that the proposed algorithm provides lower packet delay and waiting time for the unstable ONUs than that of the existing E-DBA algorithm.