The decay $Z_c(3900)^pmtoomegapi^pm$ is searched for using data samples collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energies $sqrt{s}=4.23$ and $4.26$~GeV. No significant signal for the $Z_c(3900)^pm$ is found, and upper limits at the 90% confidence level on the Born cross section for the process $e^+e^-to Z_c(3900)^pmpi^mptoomegapi^+pi^-$ are determined to be $0.26$ and $0.18$ pb at $sqrt{s}=4.23$ and 4.26 GeV, respectively.
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