Buffer management plays an important role in guaranteed frame rate (GFR) service in an asynchronous transfer mode (ATM) network. Buffer management algorithms are used to allocate appropriate space in a switch buffer for untagged GFR cells to fulfill the guaranteed minimum cell rate (MCR). Two main goals of buffer management algorithms are high throughput and high fairness index. However, these goals are compromised, that is the higher throughput gives the lower fairness index. This paper proposes a new buffer management algorithm called BADT (buffer allocation with dynamic threshold) algorithm, which uses dynamic threshold techniques for the fairness index improvement. The performance comparison of the previously proposed algorithms is shown. The simulation results show that the BADT algorithm gives the highest fairness index and still gives acceptably high throughput compared to the previously proposed algorithms.