  The Schr\"odinger equation discribing the local potential model of a strong
$\pi^+\pi^-$-interaction was studied. The influence of the strong
$\pi^+\pi^-$-interaction of the behaviour of pionium nS-state wave functions at
small distances is studied both analytically (perturbatively) and numerically.
It is shown that in the whole the accounting of strong interaction results in
multiplying pure Coulomb pionium wave functions by some function is practically
independent of the value of the principal quantum number n. Due to this reason,
the n-independence of probability of $\pi^+\pi^-$-atom production in nS-state
remains the same as in the case of a pure Coulomb $\pi^+\pi^-$-interaction.
