A random amorphous copolyester is synthesized by using diacid monomers and diol monomers. The random amorphous copolyester has a structure of the formula (I): ##STR00001## wherein R.sub.1, R.sub.2 is an aromatic or aliphatic monomer, A is 0-0.8, B is 0-0.8, C is 0-1, D is 0-1, E is 0-0.8, F is 0-0.8, C+D<0.2 and A+B+E+F<0.8. The diacid monomer comprises TPA and an aromatic or aliphatic diacid monomer, the diol monomer comprises EG, 1,3 and 1,4-CHDM, and an aromatic or aliphatic diol monomer.