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A new D3h symmetry adapted approach to accurate calculation of high-lying rovibrational (J>0) states of floppy X3 triatomic molecules is presented, extending our recent work on J=0 bound states of D3h triatomics [Z. Bacˇic and J. Z. H. Zhang, Chem. Phys. Lett. 184, 513 (1991)]. Three sets of Jacobi coordinates are employed, allowing construction of basis sets with full S3 permutation symmetry of the three identical nuclei. Inclusion of S3 symmetry reduces substantially the size of the final matrix eigenvalue problem and the computational effort involved. It also assures unambiguous, correct symmetry assignment of the calculated rovibrational levels. Our method is especially suitable for rotating D3h molecules with strongly coupled large amplitude motions of the three atoms. An efficient quasiadiabatic diagonalization and truncation scheme is incorporated into our methodology. Application to H+3 for J=1 produced the total of 426 well converged, symmetry assigned states up to ∼24 000 cm-1 above the ground state, far more than in any previous calculation for rotating H+3. [ABSTRACT FROM AUTHOR]