We show that the dominant Gamow-Teller part, M(GT)(0 nu), of the nuclear matrix element governing the neutrinoless beta beta decay is related to the matrix element M(cl)(2 nu) governing the allowed two-neutrino beta beta decay. That relation is revealed when these matrix elements are expressed as functions of the relative distance r between the pair of neutrons that are transformed into a pair of protons in the beta beta decay. Analyzing this relation allows us to understand the contrasting behavior of these matrix elements when A and Z is changed; while M(GT)(0 nu) changes slowly and smoothly, M(2 nu) has pronounced shell effects. We also discuss the possibility of phenomenological determination of the M(cl)(2 nu) and from them of the M(GT)(0 nu) values from the experimental study of the beta(+) strength functions.