It is shown that electron relaxation in an emitter-type point contact strongly affects the position of the first line of transverse electron focussing (EF) in Bi on the magnetic field scale. As a result, the energy of electrons leaving the point contact region is lower than the energy eV determined by the voltage applied to the point contact. In the case of strong currents, the intrinsic field of the current also affects the position of the EF line. The additional shift of the EF line under the action of this factor depends on V nonlinearly in view of strong nonlinearity of the current–voltage characteristics of Bi point contacts. It is shown that this nonlinearity can be explained by an increase in the concentration of charge carriers in the point contact region under the action of the gradient of potential distribution and interband tunneling. These mechanisms give an accurate description of the nonlinearity of the current–voltage characteristics of Bi point contacts.