A fully relativistic extension of the variational principle with the modified test function for the Spitzer function with momentum conservation in the electron–electron collision is investigated in uniformly magnetized plasma. The term of the momentum conserving constraint in Hirshman's variational calculation is studied. The model developed is extended for arbitrary temperatures and covers exactly the asymptotic for when , and the results obtained are suited to facilitate the development of a rigorous variational formulation of current drive efficiency in tokamak plasma.