As we know, Bondi derives the Lorentz transformations (LT) via the radar detection of the space-time coordinates of a distant event. Once derived from other starting points the LT should account for the results obtained by Bondi expressing them as a function of the Doppler factor D=sqrt[(1+b)/(1-b)] which can be derived without using the LT (b=V/c). The outgoing radar signal generates the event E(x,y=0,t=x/c) when detected from I and E'(x'=ct',y'=0,t'=x'/c). In accordance with the LT we have x=(x'+cbt')/sqrt(1-b^2). (1) But b=(D^2-1)/1+D^2 sqrt(1-b^2)=2D/(1+D^2) with which (1) becomes x=[x'(1+D^2)+ct'(D^2-1)]/2D=Dx'=Dct' (2) In a simillar way we obtain t=[(1+D^2)x'+(D^2-1)x'/c]/2D=Dt'=Dx'/c. (3) If the event is generated by a tardyon moving with speed u(u') the generated events are E(x=ut,y=0,t=x/u) and E'(x'=u't',y'=0,t'=x'/u') and the corresponding LT could be espressed again as a function of D. Do you find flows above? Do you consider that it could be a good exercise for the beginner teaching him to handle the LT? Thanks in advance for your answers.