In this letter we present a mechanism in which new nonperturbative sol
utions of quantum electrodynamics in four dimensions is found. Two non
perturbative solutions are found for approximate Schwinger-Dyson equat
ions. The mass ratio of the three solutions (one of them is the ordina
ry solution) is approximately 1 : (8 pi/alpha)(2/3) : 8 pi/alpha, whic
h is close to the realistic mass ratio of e(-), mu(-) and tau(-).