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In recent years Internet access over a DSL has experienced continuous growth. Recent technological advances have increased the potential capacity of the telephone operators' access networks, which were originally intended only to provide a POTS. However, due to an imperfect balance between the twisted pair channels, different noises occur on the telephone lines. In this paper we apply Hadamard transform instead of FFT to ADSL system with 129 taps noisy channel. We did not use any cyclic prefix. The results of simulation show that Hadamard have better performance (especially BER) with respect to FFT. We introduce the new non-rectangular QAM that with FHT has better performance (in BER) with respect to rectangular QAM.