Highly accurate Gaussian-type function basis sets are developed for 103 atoms from H (atomic number Z = 1) to Lr (Z = 103). Choosing the last atoms of the seven periods and referring to the numerical Hartree-Fock total energies, the sizes of the present sets are so determined that the total energy errors are less than 1 millihartree. The average total energy error over the 103 atoms is only 0.79 millihartrees and the maximum error is 1.47 millihartrees for the Zn atom, indicating that the new sets are well-balanced throughout the atoms in the periodic table. The basis sets are tested for the GdF molecule.