  The stretching and bending vibrations of methane are studied in the framework
of a symmetry-adapted algebraic model. The model is based on the realization of
the one-dimensional Morse potential in terms of a $U(2)$ algebra. For the 44
observed energies we obtain a fit with a r.m.s. deviation of 1.16 cm$^{-1}$
which is an order of magnitude more accurate than previous algebraic
calculations.
