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Evidence has recently been presented for the existence of a dibaryon of mass 2380 MeV/c2 and width 70 MeV/c2, which decays strongly into the dπ0π0 channel [M. Bashkanov, et al., Phys. Rev. Lett. 102 (2009) 052301; P. Adlarson, et al., arXiv:1104.0123]. The decay rate of such a hypothesised dibaryon into the {pn}I=0π0π0 channel is estimated in a weakly model-dependent way by using final state interaction theory. It is shown that, if the resonance exists, it should show up as strongly in this channel as in dπ0π0. The sum of the two decay modes would saturate most of the inelasticity predicted in the relevant partial waves in the 2380 MeV/c2 region.