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The bandwidth limitation of wideband (WB) audio systems degrades the subjective quality and naturalness of audio signals. In this paper, a new method for blind bandwidth extension of WB audio signals is proposed based on non-linear prediction and hidden Markov model (HMM). The high-frequency (HF) components in the band of 7–14 kHz are artificially restored only from the low-frequency information of the WB audio. State-space reconstruction is used to convert the fine spectrum of WB audio to a multi-dimensional space, and a non-linear prediction based on nearest-neighbor mapping is employed in the state space to restore the fine spectrum of the HF components. The spectral envelope of the resulting HF components is estimated based on an HMM according to the features extracted from the WB audio. In addition, the proposed method and the reference methods are applied to the ITU-T G.722.1 WB audio codec for comparison with the ITU-T G.722.1C super WB audio codec. Objective quality evaluation results indicate that the proposed method is preferred over the reference bandwidth extension methods. Subjective listening results show that the proposed method has a comparable audio quality with G.722.1C and improves the extension performance compared with the reference methods.