It is generally believed that Majorana’s paper [4] describes particles which have no antiparticles. A thorough analysis have shown that this paper gives rise to the questions the answers to which have not been realized up to now. By the Majorana equation we mean the equation that describes stable, massive, and neutral leptons. Fulfillment of these three requirements leads strictly and unambiguously to the conclusion that the Majorana equation describes a pair of stable, massive, and neutral leptons, a particle and an antiparticle. This is similar to the Dirac equation, but the spin properties of the leptons of this type differ from the spin properties of the electron or positron.