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This paper studies the constant amplitude codebook based feedback scheme for Tomlinson-Harashima Precoding (THP) in multi-user multiple-input-multiple-output (MU-MIMO) systems. Conventional THP precoding scheme uses non-constant amplitude codebook to encapsulate channel direction information as well as channel amplitude information. In this paper we first prove that channel amplitude information is not necessary in the user channel quantization for THP precoding with limited feedback, thus in the proposed scheme we can apply constant amplitude codebook for channel quantization. Because we do not waste feedback bits to represent the channel amplitude information in the codebook applied, the proposed scheme achieves better quantization accuracy leading to better sum-rate performance compared with the conventional one. Our analysis and the validity of the proposed scheme are verified by numerical simulations.