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The Improved time sliding window based Three Color Marker (ItswTCM), improves bandwidth fairness in Differentiated Services (DiffServ) network by providing a proportional fair share of the excess network bandwidth among aggregates, when the aggregates are of Assured Service (AS) class. However, unfairness arises, when aggregate of Best effort (BE) service class exists along with AS class in the DiffServ network. In this paper, an attempt has been made to circumvent the above unfairness by a modified approach in the buffer management at the core of the DiffServ network. In the proposed scheme, packets corresponding to the AS and BE service classes are separated in two queues and serviced using priority scheduling algorithm. Simulations with the proposed scheme have been carried out using NS-2 and the results show that the buffer management at the core provides better goodput and fair distribution of excess bandwidth in all cases.