In the experiment with the SND detector at the VEPP-2000 $e^+e^-$ collider the cross section for the process $e^+e^-toetapi^+pi^-$ has been measured in the center-of-mass energy range from 1.22 to 2.00 GeV. Obtained results are in agreement with previous measurements and have better accuracy. The energy dependence of the $e^+e^-toetapi^+pi^-$ cross section has been fitted with the vector-meson dominance model. From this fit the product of the branching fractions $B(rho(1450)toetapi^+pi^-)B(rho(1450)to e^+e^-)$ has been extracted and compared with the same products for $rho(1450)toomegapi^0$ and $rho(1450)topi^+pi^-$ decays. The obtained cross section data have been also used to test the conservation of vector current hypothesis.
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