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The one-dimensional Schrödinger equation with the point potential in the form of the derivative of Dirac's delta function, λδ ′ (x) with λ being a coupling constant, is investigated. This equation is known to require an extension to the space of wave functions ψ(x) discontinuous at the origin under the two-sided (at x = ±0) boundary conditions given through the transfer matrixHowever, the recent studies, where a resonant non-zero transmission across this potential has been established to occur on discrete sets {λ n } ∞ n=1 in the λ-space, contradict to these boundary conditions used widely by many authors. The present communication aims at solving this discrepancy using a more general form of boundary conditions.