The cross-section for the\(\pi ^ ++ ^4 He \to \pi ^ -+ 4p\) reaction has been measured with a high-pressure helium streamer chamber triggered by a scintillation counter hodoscope. Measurements were made for angles between 25° and 165°. Supposing the angular distribution of the secondary meson to be isotropic, we obtained the following total cross-section for the double charge exchange:\(\sigma _{tot}= \left( {0.30 \pm 0.15} \right) \cdot 10^{ - 27} cm^2 \). The obtained value turned out to be somewhat smaller than expected from calculations using the pair correlation model.