By applying a method of virtual quanta we derive formulae for relativistic non-thermal bremsstrahlung radiation from relativistic electrons as well as from protons and heavier particles with power-law momentum distribution $N(p)dp = k p^{-q} dp.$ We show that emission which originates from an electron scattering on an ion, represents the most significant component of relativistic non-thermal bremsstrahlung. Radiation from an ion scattering on electron, known as inverse bremsstrahlung, is shown to be negligible in overall non-thermal bremsstrahlung emission. These results arise from theory refinement, where we introduce the dependence of relativistic kinetic energy of an incident particle, upon the energy of scattered photon. In part, it is also a consequence of a different mass of particles and relativistic effects. ; Comment: 17 pages, 1 figure, accepted for publication in IJMPA