The Lead Field Analysis (LFA) algorithm, a new computational technique for the calculation of potentials on the surface of a realistic head shaped volume conductor model based on the Boundary Element Method and the Reciprocity Theorem, is presented. The new algorithm, in comparison to the Standard Boundary Element Method, offers improved computational efficiency and lower storage requirements. It also yields more accurate surface potential results in the face of varying dipole source locations for a head shape Boundary Element model with a given number of nodes. Additionally, the algorithm results in quasi-analytic expressions of the derivatives of the surface potential with respect to the location of the sources, allowing the use of optimization techniques with better convergence properties. A set of simulations demonstrating the increased robustness of the LFA Algorithm in the face of varying dipole source parameters is also described.