  The process $e^+e^- \to \omega\pi^0 \to \pi^+\pi^-\pi^0\pi^0$ is studied in
the center-of-mass energy region $1.05-2.00$ GeV using data with an integral
luminosity of about 35 pb$^{-1}$ collected with the SND detector at the
VEPP-2000 $e^+e^-$ collider. In the energy range under study, the value of the
measured Born cross section varies from 0.7 to 18 nb. The statistical
uncertainty of the cross section is $2-23$%, while the systematic uncertainty
is in the range of $3.0-14.2$%. The results are consistent with previous
measurements but have better accuracy.
