The paper proposes a new parameterization, named NL3, for the Lagrangian density of relativistic mean field (RMF) theory, aimed at improving the description of nuclear properties, especially those far from beta-stability. The new parameterization is derived through a multi-parameter fit using experimental data on charge radii, binding energies, and neutron radii of spherical nuclei. The fit includes ten nuclei, with additional nuclear matter properties as constraints. The new parameter set is compared with existing ones, NL1 and NL-SH, showing better agreement with experimental data for various nuclear properties, including superdeformed minima in the Hg region. The NL3 parameterization is also applied to detailed calculations of rare-earth and actinide nuclei, demonstrating excellent agreement with experimental results. The paper concludes that NL3 provides a significant improvement over existing parameterizations in describing nuclear masses, deformation properties, and isoscalar monopole energies.The paper proposes a new parameterization, named NL3, for the Lagrangian density of relativistic mean field (RMF) theory, aimed at improving the description of nuclear properties, especially those far from beta-stability. The new parameterization is derived through a multi-parameter fit using experimental data on charge radii, binding energies, and neutron radii of spherical nuclei. The fit includes ten nuclei, with additional nuclear matter properties as constraints. The new parameter set is compared with existing ones, NL1 and NL-SH, showing better agreement with experimental data for various nuclear properties, including superdeformed minima in the Hg region. The NL3 parameterization is also applied to detailed calculations of rare-earth and actinide nuclei, demonstrating excellent agreement with experimental results. The paper concludes that NL3 provides a significant improvement over existing parameterizations in describing nuclear masses, deformation properties, and isoscalar monopole energies.