An efficient method is described for generating a fragmented, permutationally invariant polynomial basis to fit electronic energies and, if available, gradients for large molecules. The method presented rests on the fragmentation of a large molecule into any number of fragments while maintaining the permutational invariance and uniqueness of the polynomials. The new approach improves on a previous one reported by Qu and Bowman by avoiding repetition of polynomials in the fitting basis set and speeding up gradient evaluations while keeping the accuracy of the PES. The method is demonstrated for CH3-NH-CO-CH3 (N-methylacetamide) and NH2-CH2-COOH (glycine).