Digital audio data-hiding systems have great potential for concealing data in a digital audio signal. The performance of the proposed system has been improved over the years to increase the imperceptibility, robustness, and embedding capacity of the system. However, as the demand for new applications of data-hiding systems increases, there is a need to develop new, distinct techniques. This study proposes a novel modulation technique, called rounding modulation, for a transparent digital audio-data hiding system. The goal was to create a digital audio data-hiding system with high imperceptibility that has the capacity of delivering a large payload of secret data. This technique was then combined with the traditional phase-shift keying modulation system to demonstrate the possibility of combining it with other modulation systems. The simulations showed that the proposed technique is capable of embedding a large amount of data while keeping the changes in the audio file imperceptible to the human auditory system.