Reversible data hiding is a technique where hidden data is embedded in host data, such that the consistency of the host is perfectly preserved and the host data is restored during the extraction process of the hidden data. Herein, improvements to the conventional technique for reversible data hiding of audio waveforms are proposed. As no location map is required to prevent amplitude overflow, the proposed method achieves a storage capacity of nearly 1 bit per sample of payload data. The proposed method is superior in terms of having a smaller loss of payload data and little objective quality degradation on average. Concealment of payload within the host data is also better than when using the conventional method.