Structured　frames　have　interested　many　mathematicians　and　engineers　due　to　their　potential　applications.　This　paper　addresses　the　theory　of　K-frames　associated　with　unitary　groups.　Let　U　be　a　unitary　group　for　a　separable　Hilbert　space　94.　Given　a　K-frame　generator　U　for　U,　we　present　an　explicit　expression　of　all　K-dual　Bessel　generators　of　eta　for　U　under　two　cases,　and　simultaneously,　prove　that　its　canonical　K-dual　Bessel　generator　corresponds　to　the　most　economic　presentation　of　the　element　from　the　range　of　K.　(C)2019　Elsevier　Inc.　All　rights　reserved.