We search for a new gauge boson Z′ that couples only to heavy leptons and their corresponding neutrinos in the process e+e-→Z′(→μ+μ-)μ+μ-, using a 643 fb-1 data sample collected by the Belle experiment at or near the ϒ(1S,2S,3S,4S,5S) resonances at the KEKB collider. While previous searches for Z′ performed a data-based estimation of the initial state radiation effect, our search for the Z′ is the first to include effects due to initial state radiation in the signal simulated samples that were used in estimating the detection efficiency. No signal is observed in the Z′ mass range of 0.212-10 GeV/c2, and we set an upper limit on the coupling strength, g′, constraining the possible Z′ contribution to the anomalous magnetic dipole moment of the muon. © 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.