A puzzle has long existed for the $alpha$-cluster content in the near-threshold 7.54 MeV state of $^{10}$Be. A new measurement was conducted to measure the cluster-decay partial width of this state, using the reaction $rm{^9Be}(rm{^9Be}, rm{^{10}Be}^{*} rightarrow alpha + rm{^6He})rm{^8Be}$ at 45 MeV beam energy. Special measures were taken to reduce the strong near-threshold background. The neutron-decay strength was also obtained based on the three-fold coincident measurement. A cluster-decay branching ratio of $(4.04 pm 1.26)times 10^{-4}$ is obtained, resulting in a reasonably large $alpha$-cluster spectroscopic factor. The present work confirms the formation of the $sigma$-bond molecular rotational band headed by the 6.18 MeV state in $^{10}$Be.
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