A new spectroscopic model is developed for theoretical predictions of vibration-rotation line positions and line intensities of the methane molecule. Resonance coupling parameters of the effective polyad Hamiltionians were obtained via high-order contact transformations (CT) from ab initio potential energy surface. This allows converging vibrational and rotational levels to the accuracy of best variational calculations. Average discrepancy with centers of 100 reliably assigned experimental bands up to the triacontad range was 0.74 cm(-1) and 0.001 cm(-1) for GS rotational levels up to J = 17 in direct CT calculations without adjustable parameters. A subsequent "fine tuning" of the diagonal parameters allows achieving experimental accuracy for about 5600 Dyad and Pentad line positions, whereas all resonance coupling parameters were held fixed to ab initio values. Dipole transition moment parameters were determined from selected ab initio line strengths previously computed from a dipole moment surface by variational method. New polyad model allows generating a spectral line list for the Dyad and Pentad bands with the accuracy similar to 10(-3) cm(-1) for line positions combined with ab initio predictions for line intensities. The overall integrated intensity agreement with Hitran-2008 empirical database is of 4.4% for the Dyad and of 1.8% for the Pentad range.