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Most state-of-the-art speech enhancement (SE) techniques prefer to enhance utterances in the frequency domain rather than in the time domain. However, the overlap-add (OLA) operation in the short-time Fourier transform (STFT) for speech signal processing possibly distorts the signal and limits the performance of the SE techniques. In this study, a novel SE method that integrates the discrete wavelet packet transform (DWPT) and a novel subspace-based method, robust principal component analysis (RPCA), is proposed to enhance noise-corrupted signals directly in the time domain. We evaluate the proposed SE method on the Mandarin hearing in noise test (MHINT) sentences. The experimental results show that the new method reduces the signal distortions dramatically, thereby improving speech quality and intelligibility significantly. In addition, the newly proposed method outperforms the STFT-RPCA-based speech enhancement system.