To improve the accuracy of the fragment molecular orbital method (FMO), we introduce a new fragmentation scheme based on using frozen orbitals to describe fractioned bonds. By applying this scheme to a set of polyalanine systems of up to 40 residues for the alpha-helix and beta-strand isomers, we established its accuracy, which is considerably improved compared to the original hybrid orbital projection method used for detaching bonds in FMO. For instance, at the two-body FMO expansion with the 6-311G* basis set, the error was typically reduced 2-4 times, and for 6-31G* the accuracy increase was even larger (10 times in terms of the maximum error). For the Trp-cage protein (PDB file 1L2Y) with many charged residues, a fairly large error was observed, which was shown to become small with a larger fragment size or at the three-body level. Consequently, we applied the new scheme to the adsorption of toluene and phenol on a faujasite zeolite, and we demonstrated that good accuracy can be achieved in reproducing ab initio results.