[en] A computational investigation of β-HP_4N_7 system is accurately performed using the density functional theory formalism coupled with quantum theory of atoms in molecules. The aim of this work is to understand the behavior of β-HP_4N_7 under compression. At ambient conditions, the N atoms occupy around 81% of the unit cell volume; for this reason the N atoms are the ones contributing significantly to the bulk properties. The particular tetrahedron (PN_4) connection promotes high flexibility to this structure. The atoms composing the solid show significant differences in their compressibilities. The high compressibility (or low resistence to pressure) of the N atoms indicates that the reorganization of these atoms is the key in the densification process that takes place when pressure is increased. When compresing the β-HP_4N_7 from 0 to 130 GPa the formation of PN_6 units is observed, leading to a phase transition. The analysis of the elastic constants reveals the stability of this new phase at 110 GPa. This study shows that β-HP_4N_7 could be a potential candidate for high pressure synthesis of new phases where P atoms would be 6-fold coordinated. (paper)