The paper describes a new method for the calculation of the Sommerfeld screening parameter σ₁. It requires neither the knowledge of the energy separations of spin doublet levels nor is it based on the application of the Hertz law. The only data required for the calculation are the experimental energy values of the level concerned for the series of elements belonging to the same subshell in which the element in the question is situated. As an illustration the values of σ₁ are calculated for the L₁, L₂ and L₃ levels for elements belonging to the 4f subshell and these are found to be in excellent agreement with those published earlier by Gokhale and Misra. The method brings out the constancy of σ₁ (L₂L₃)−σ₁(L₁) in a natural way and may thus be regarded as providing theoretical explanation of the Hertz law.