In　a　recent　work　(Shao　et　al.;　2009),　a　nonconsensus　opinion　(NCO)　model　was　proposed,　where　two　opinions　can　stably　coexist　by　forming　clusters　of　agents　holding　the　same　opinion.　The　NCO　model　on　lattices　and　several　complex　networks　displays　a　phase　transition　behavior,　which　is　characterized　by　a　large　spanning　cluster　of　nodes　holding　the　same　opinion　appears　when　the　initial　fraction　of　nodes　holding　this　opinion　is　above　a　certain　critical　value.　In　the　NCO　model,　each　agent　will　convert　to　its　opposite　opinion　if　there　are　more　than　half　of　agents　holding　the　opposite　opinion　in　its　neighborhood.　In　this　paper,　we　generalize　the　NCO　model　by　assuming　that　each　agent　will　change　its　opinion　if　the　fraction　of　agents　holding　the　opposite　opinion　in　its　neighborhood　exceeds　a　threshold　T　(T≥0.5).　We　call　this　generalized　model　as　the　NCOT　model.　We　apply　the　NCOT　model　on　different　network　structures　and　study　the　formation　of　opinion　clusters.　We　find　that　the　NCOT　model　on　lattices　displays　a　continuous　phase　transition.　For　random　graphs　and　scale-free　networks,　the　NCOT　model　shows　a　discontinuous　phase　transition　when　the　threshold　is　small　and　the　average　degree　of　the　network　is　large,　while　in　other　cases　the　NCOT　model　displays　a　continuous　phase　transition.　©　2015　Elsevier　B.V.　All　rights　reserved.