Scalp electric potentials (electroencephalograms) and extracranial magnetic fields (magnetoencephalograms) are due to the primary (impressed) current density distribution that arises from neuronal postsynaptic processes. A solution to the inverse problem--the computation of images of electric neuronal activity based on extracranial measurements--would provide important information on the time-course and localization of brain function. In general, there is no unique solution to this problem. In particular, an instantaneous, distributed, discrete, linear solution capable of exact localization of point sources is of great interest, since the principles of linearity and superposition would guarantee its trustworthiness as a functional imaging method, given that brain activity occurs in the form of a finite number of distributed hot spots. Despite all previous efforts, linear solutions, at best, produced images with systematic nonzero localization errors. A solution reported here yields images of standardized current density with zero localization error. The purpose of this paper is to present the technical details of the method, allowing researchers to test, check, reproduce and validate the new method.