According to a thermomechanical treatment process for a titanium alloy including between 23 and 27% niobium in atomic proportion, between 0 and 10% zirconium, and between 0 and 1% oxygen, nitrogen and/or silicon, the following steps are performed:a) an increase of a sample of the alloy to a temperature higher than 900° C.,b) a fast quench,c) a severe cold strain,d) an ageing treatment at a temperature included between 200 and 600° C., the time of the ageing treatment being included between 10 seconds and 10 minutes.Alloy obtained by this process and prostheses made from such an alloy.