A global potential energy surface (PES) for the adiabatic ground state of the H-4 system which fit published ab initio data [Boothroyd, et al. J. Chem. Phys. 95, 4331 (1991)] at a quantitative level has been obtained (root-mean-square error about 2 mhartree or 1-2 kcal/mol), and without any quantity of ad hoc character, preserving the accuracy of the ab initio points. The global fitting procedure used here is an extension of the corresponding procedure for triatomic systems including the functional form previously proposed by the authors. The global H-4 PES obtained here is totally symmetric with respect to permutations of the hydrogen atoms and satisfies the criteria needed to be used in scattering calculations.