Due　to　the　application　in　reliable　communication,　reliable　broadcasting,　secure　message　distribution,　etc.,　node/edge-independent　spanning　trees　(ISTs)　have　attracted　much　attention　in　the　past　twenty　years.　However,　node/edge　conjecture　is　still　open　for　networks　with　node/edge-connectivity　≥　5.　So　far,　results　have　been　obtained　on　a　lot　of　special　networks,　but　only　a　few　results　are　reported　on　the　line　graphs　of　them.　Hypercubes　play　important　roles　in　parallel　computing　systems,　and　the　line　graphs　of　which　have　been　recently　adopted　for　the　architectures　of　data　center　networks.　Since　the　line　graph　of　n-dimensional　hypercube　Qn,　L(Qn),　is　(2n−2)-regular,　whether　there　exist　2n−2　node-ISTs　rooted　at　any　node　on　L(Qn)　is　an　open　question.　In　this　paper,　we　focus　on　the　problem　of　constructing　node-ISTs　on　L(Qn).　Firstly,　we　point　out　that　L(Qn)　can　be　partitioned　into　2n−1　complete　graphs.　Then,　based　on　the　complete　graphs　and　n−1　node-ISTs　rooted　at　0　on　Qn−10,　we　obtain　an　＇independent　forest＇　containing　2n−2　trees　on　L(Qn).　Furthermore,　we　present　an　O(N)　time　algorithm　to　construct　2n−2　node-ISTs　rooted　at　node　[0,　2n−1]　isomorphic　to　each　other　on　L(Qn)　based　on　the　independent　forest,　where　N=n×2n−1　is　the　number　of　nodes　on　L(Qn).　In　addition,　we　point　out　that　the　2n−2　node-ISTs　on　L(Qn)　is　a　new　method　to　prove　the　node/edge-connectivity　and　the　upper　bound　of　(2n−2)-node/edge-wide-diameter　of　L(Qn).　©　2019　Elsevier　Inc.