A valence bond study of the potential energy surface for methane CH4--> CH3 + H is performed at the 6-31G level using (i) a valence bond self-constituent field (VB-SCF) method; (ii) a valence bond configuration interaction (VBCI) method; and (iii) an antisymmetrized product of strong-orthogonal geminals (APSG) method (also in VB form). The calculations show that, although the energies are somewhat inferior (on an absolute scale) to those obtained in very large CI calculations, the VB reduced potential energy surfaces behave better, in the intermediate range 2-3 Angstrom, than those obtained using (i) the Moller-Plesset fourth-order perturbation (MP4) approximation, (ii) configuration interaction with all singles and doubles (CISD), and (iii) coupled clusters with all singles and doubles (CCSD). The results are in very good agreement with those obtained from multi-reference configuration interaction (MR-CISD) calculations. The lower absolute energies obtained in the very extensive CI calculations indicate a better description of electron correlation, both in the molecule and in its dissociation products, but evidently they do not imply a better overall description of the PE surface. The remarkable fact is that a single VB structure, with carefully optimized orbitals, provides an excellent description of the whole dissociation process.