True random number generators (TRNG) are important counterparts to pseudorandom number generators (PRNG), especially for high security applications such as cryptography. They produce unpredictable, non-repeatable random sequences. However, most TRNGs require specialized hardware to extract entropy from physical phenomena and tend to be slower than PRNGs. These generators usually require post-processing algorithms to eliminate biases but in turn, reduces performance. In this paper, a new post-processing method based on hyperchaos is proposed for software-based TRNGs which not only eliminates statistical biases but also provides amplification in order to improve the performance of TRNGs. The proposed method utilizes the inherent characteristics of chaos such as hypersensitivity to input changes, diffusion, and confusion capabilities to achieve these goals. Quantized bits of a physical entropy source are used to perturb the parameters of a hyperchaotic map, which is then iterated to produce a set of random output bits. To depict the feasibility of the proposed post-processing algorithm, it is applied in designing TRNGs based on digital audio. The generators are analyzed to identify statistical defects in addition to forward and backward security. Results indicate that the proposed generators are able to produce secure true random sequences at a high throughput,which in turn reflects on the effectiveness of the proposed post-processing method.