  An impermeable barrier at $r=r_{cl}$ in the effective potential of the
relativistic Schr\"odinger-type equation leads to exclusion of the range $0
\leq r < r_{cl}$ from the wave function domain. Based on duality of the
Schr\"odinger-type equation and the Dirac equation, a similar exclusion should
be made in the wave functions domain of the Dirac equation. As a result, we
obtain new solutions to the Dirac equation in the Coulomb repulsive field.
Calculations show that depending on working parameters, at distances of several
fractions or units of the Compton wavelength of the fermion from $r=r_{cl}$ new
solutions almost coincide with the standard Coulomb functions of the continuous
spectrum. Practically, matrix elements with new solutions will coincide to a
good accuracy with standard matrix elements with the Coulomb functions of the
continuous spectrum. Our consideration is methodological and helpful for
discussing further development of quantum theory.
