The wavefunctions for neon and its positive ion which are reported here appear to be more accurate than any which have previously been available. This is because full correlation for all pairs of electrons has been evaluated by the particular transcorrelated matrix equations recently derived for wavefunctions with explicit electronic correlation. The error in the predicted ionization potential of neon obtained by the difference of the energies of the two calculations is about 1 kcal/mole, which can be regarded as reasonable chemical accuracy. The errors in the total correlation energies are about 6%. It is considered that this method of calculation shows greater possibilities for the accurate prediction of the energies of atomic and molecular systems than those previously available.