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A novel technique for the application of the wavelet transform (WT) in noisy narrow-bandwidth systems is presented. The proposed technique for signal processing is, by contrast to other previous approaches, a non-degenerated application of the WT, combined with the non-linear process of thresholding. The application of such processing in a narrow-bandwidth signals field such as ultrasonics, is presented. The results show that a noise-cleaned signal, with altered envelope, but with unaffected timing characteristics is achieved. The accuracy of time-of-flight measurements in ultrasonic systems is considerably improved since zero-crossings of the incoming echo signal retain their positions.