A new inversion coordinate is defined for ammonia as a function of the valence angles. Its square is similar to the often used totally symmetric bending displacement coordinate for the pyramidal XY3-type molecules. We have used this in a two-dimensional calculation including the totally symmetric stretching and the inversion mode. A conventional symmetrized internal coordinate is employed for the symmetric stretch. A two-dimensional potential energy surface is calculated using the ab initio CCSD(T) method together with the aug-cc-pVTZ, cc-pVQZ, and aug-cc-pVQZ basis sets. The corresponding eigenvalues are calculated variationally using a Morse oscillator basis set for the stretch and a harmonic oscillator basis set for the inversion. A good agreement is obtained between the calculated and 22 experimental inversion levels, 9 of (NH3)-N-14 and the others involving 4 other isotopomers ((ND3)-N-14, (NH3)-N-15, (ND3)-N-15, and (NT3)-N-14). With the aug-cc-pVTZ basis, a mean absolute error of 5.0 cm(-1) is obtained whereas with the aug-cc-pVQZ basis set the error becomes 7.9 cm(-1).