The relativistic modified formula for the energy loss of the relativistic electron beam due to binary electron–electron collisions is obtained. Another important energy loss mechanism, the excitation of Langmuir collective plasma oscillation, is also treated within the relativistic framework. Then the relevant physics parameters in the fast-ignitor scenario, including the continuous winded range, the maximum penetration depth and the stopping time, have been calculated. The results obtained are much better than those from non-relativistic cases and even partially relativistic modified theories. Thus, we re-examine theoretically the possibility of igniting hot spots in a super-compressed deuterium–tritium plasma.