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The design of a TCP-friendly layered video multicast scheme with thin layer partitioning is studied in this research. It was shown in Nahm et al. (2003) that the cumulative layered multicast with static layers can achieve TCP-friendly network adaptation with good fairness via the usage of thin layers. However, if the layer is thinner than the scale of network fluctuation, the convergence to the target throughput may not be attainable even in the steady state. In this work, we propose a simple nonlinear preprocessing, called the minmax averaging operation, in the basic loss rate estimation algorithm, to help a TCP-friendly throughput estimation robust to network fluctuation. It is demonstrated via computer simulation that the stability of the network adaptation performance has been improved with the usage of the proposed scheme.