Bethe-Salpeter equation, for massless exchange and large fine structure constant $alpha>pi/4$, in addition to the Balmer series, provides another (abnormal) series of energy levels which are not given by the Schrodinger equation. So strong field can be created by a point-like charge $Z>107$. The nuclei with this charge, though available, they are far from to be point-like that weakens the field. Therefore, the abnormal states of this origin hardly exist. We analyze the more realistic case of exchange by a massive particle when the large value of coupling constant is typical for the strong interaction. It turns out that this interaction still generates a series of abnormal relativistic states. The properties of these solutions are studied. Their existence in nature seems possible.
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