The formation process of the well-known biomedical alloy of the Ti-21Nb-5Zr (at %) composition is studied by the hydride cycle (HC) method. TiH2 hydrides (content H-2, 4.01 wt %), ZrH2 (content H-2, 2 wt %), and NbH1.23 (content H-2, 1.31 wt %) are preliminarily synthesized by self-propagating high-temperature synthesis (SHS). The experiments are carried out in a sealed installation consisting of a quartz reactor, a furnace, and devices for controlling the vacuum and temperatures in the reactor. The reactor's temperature is gradually increased to 1000 degrees C and the sample is kept at this temperature for 30-60 min. The following reaction is investigated: 74% TiH2 + 21% NbH1.23 + 5% ZrH2 -> Ti0.74Nb0.21Zr0.05 + H-2 up arrow. As a result of the HC, the Ti0.74Nb0.21Zr0.05 beta-alloy containing about 20.2% of the alpha-phase was synthesized. Ti0.74Nb0.21Zr0.05 alloy samples without crushing in the SHS mode interacted with hydrogen (P-H = 10 atm), forming an Ti0.74Nb0.21Zr0.05H1.84 (3 wt %) alloy hydride. A high hydrogen content provides the easy dispersibility of the powder's grains into micron, submicron, and nano sizes. Ti0.74Nb0.21Zr0.05H1.84 alloy hydride can be recommended as a biomedical material for manufacturing implants. The core advantages of the HC method to synthesize the beta-type Ti0.74Nb0.21Zr0.05 alloy are shown compared to the traditional methods (induction and arc melting, etc.). The results obtained make it possible to predict the prospects of using the HC method for the synthesis of biomedical materials.