A　cut　direction,　rotated　ZY　cut　of　Lithium　Niobate　(LN),　is　studied.　LN　is　a　good　piezoelectric　crystal　and　it　can　be　used　as　substrate　of　surface　acoustic　wave　devices.　In　this　paper,　surface　acoustic　wave　equations,　including　basic　equations　and　boundary　condition　equations,　are　deduced.　According　to　these　equations　the　surface　acoustic　wave　velocities　are　systematically　calculated　using　a　circle　iterative　method　for　LN　along　different　directions　in　optimum　decoupling　acoustic　sagittal　YZ　plane.　The　electromechanical　coupling　coefficients　for　rotated　ZY　cut　LN　are　also　calculated.　The　optimum　cut　direction　of　the　LN　crystal　piece　as　substrate　of　surface　acoustic　wave　devices　is　determined　by　the　largest　electromechanical　coupling　coefficient.