Edge-Independent　spanning　trees　(EISTs)　can　be　used　in　IP　fast　rerouting　to　guarantee　recovery　from　link　failures,　as　well　as　in　data　broadcasting　in　networks　to　enhance　fault-tolerance,　bandwidth,　and　security.　The　n-dimensional　augmented　cube　AQn　is　an　important　node-symmetric　variant　of　the　n-dimensional　hypercube　Qn.　Recently,　Wang　et　al.　proposed　a　method　to　construct　2n−1　EISTs　in　AQn　(Wang　et　al.,　2017).　However,　the　height　of　the　tallest　EIST　is　no　less　than　n+2.　Since　height　is　an　important　performance　indicator　of　the　EISTs,　in　this　paper,　we　further　study　the　existence　and　construction　of　EISTs　in　augmented　cubes　with　lower　heights.　We　first　propose　a　constructive　algorithm　to　construct　2n−1　trees　rooted　at　any　node　in　AQn.　We　then　prove　the　2n−1　trees　obtained　by　the　algorithm　are　2n−1　EISTs　with　the　maximal　height　n,　and　the　time　complexity　of　the　algorithm　is　O(NlogN),　where　N=2n　is　the　number　of　nodes　in　AQn.　©　2019　Elsevier　B.V.