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In this paper, we further investigate new construction methods for uninormson bounded lattices via given uninorms. More specifically, we first constructnew uninorms on arbitrary bounded lattices by extending a given uninorm on asubinterval of the lattices under necessary and sufficient conditions on thegiven uninorm. Moreover, based on the new uninorms, we can give anothersufficient and necessary condition under which $S_{1}^{*}$ is a $t$-conorm($T_{1}^{*}$ is a $t$-norm) in \cite{SS06}. Furthermore, using closureoperators (interior operators), we also provide new construction methods foruninorms by extending the given uninorm on a subinterval of a bounded latticeunder some additional constraints and simultaneously investigate the additionalconstraints carefully and systematically. Meanwhile, some illustrative examplesfor the above construction methods of uninorms on bounded lattices areprovided.

Some further construction methods for uninorms via uninorms