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In this paper, we present a node dependent wavelet thresholding approach in order to remove strongly coloured noises from speech signals. The noise power in each node is first estimated using a recursive method. Given the voiced or unvoiced nature of the frame, the signal is expanded onto a predefined best basis. Then a infinitely smooth soft threshold is applied depending on each node of the decomposition tree. Finally the estimated clean signal is reconstructed. Experimental results on a Japanese database, for various coloured noises, demonstrate the effectiveness of the proposed method, even at low SNR. Compared with the common level dependent method, this algorithm provides better denoising results.