We investigate the pressure-induced structural phase transformation of amorphous silicon hexaboride (a-SiB6) using a constant pressure first principles approach. a-SiB6 is found to undergo a gradual phase transformation to a high-density amorphous phase (HDA) in which the average coordination number of both B and Si atoms is about 6. The HDA phase consists of differently coordinated motifs ranging from 4 to 8. B-12 icosahedra are found to persist during compression of a-SiB6 and the structural modifications primarily occur around Si atoms and in the regions linking pentagonal pyramid-like configurations to each other. Upon pressure release, an amorphous structure, similar to the uncompressed one, is recovered, indicating a reversible amorphous-to-amorphous phase change in a-SiB6. When the electronic structure is considered, the HDA phase is perceived to have a wider forbidden band gap than the uncompressed one.