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In this paper, we propose an algorithm to improve the naturalness of the reconstructed glossectomy patient's speech that is generated by voice conversion to enhance the intelligibility of speech uttered by patients with a wide glossectomy. While existing VC algorithms make it possible to improve intelligibility and naturalness, the result is still not satisfying. To solve the continuing problems, we propose to directly modify the speech waveforms using a spectrum differential. The motivation is that glossectomy patients mainly have problems in their vocal tract, not in their vocal cords. The proposed algorithm requires no source parameter extractions for speech synthesis, so there are no errors in source parameter extractions and we are able to make the best use of the original source characteristics. In terms of spectrum conversion, we evaluate with both GMM and DNN. Subjective evaluations show that our algorithm can synthesize more natural speech than the vocoder-based method. Judging from observations of the spectrogram, power in high-frequency bands of fricatives and stops is reconstructed to be similar to that of natural speech.