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We analyze new QCD sum rules for the pion wave function $\phi_{\pi}(x)$,obtained recently by A.V. Radyushkin in the framework of the non-local vacuumcondensates method for non-diagonal correlators, and suggest a new approach forextracting wave functions of the $\pi$-meson and of its first resonances. As aresult we obtain approximately the same form of the pion wave function by usingtwo different methods and for two different ansatzes of non-local quarkcondensates. We predict the mass of the $\pi'$-resonance and obtain the form ofits wave function. The first method uses integrated (in a sense) properties ofansatzes and may be considered as an alternative to traditional borel SR.Comment: LATEX, 15 pages, 6 figures, revised version contains corrected  reference

QCD sum rules for pion wave function revisited