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Congestion control is an important issue in resource management of ATM networks. It is therefore necessary to develop stable rate-based ABR congestion control schemes that minimise or prevent cell loss, require small buffer sizes and minimise end to end delay. Although there are some excellent congestion control methods reported in the literature that use formal control theory, the issues of ensuring minimum cell rate (MCR) and guaranteeing global asymptotic stability have not been handled successfully. In a recent paper, we proposed a method to alleviate these problems. However, the development of the controller and the proof of the stability was based on an approximate model of the system. When the cell rate within a time slot is not uniform, this model does not hold true. In this paper, we propose a parameter adaptive congestion avoidance method that uses a one step ahead predictor. It has been shown analytically and by simulation that the proposed method performs better than our former method while guaranteeing global asymptotic stability. However, as the controller is adaptive, the computational burden is increased.