A new parameterization for the Lagrangian density of relativistic mean field (RMF) theory is proposed, which provides an excellent description of nuclear properties, including those far from the valley of beta-stability and recently measured superdeformed minima in the Hg region. RMF theory, with a limited number of parameters, successfully describes nuclear structure properties, including anomalous kinks in isotope shifts, giant resonances, and superdeformed rotational bands. However, existing parameterizations like NL1 and NL-SH have limitations, such as over-binding along the beta-stability line and poor description of superdeformed minima in Hg isotopes. The new parameterization, NL3, addresses these issues by improving the description of nuclear properties, including charge radii, binding energies, and deformation characteristics. NL3 predicts a nuclear matter incompressibility between that of NL1 and NL-SH, with an asymmetry energy closer to NL-SH. It successfully reproduces experimental data for nuclear masses, charge radii, and deformation properties of rare-earth and actinide nuclei. NL3 also accurately describes isoscalar giant monopole resonances in Pb and Zr nuclei, which previous parameterizations failed to do. The new parameterization is validated through detailed calculations for Sn isotopes and other nuclei, showing improved results over NL1 and NL-SH. The study concludes that NL3 provides a more accurate description of nuclear properties and can be used in future investigations alongside other parameterizations.A new parameterization for the Lagrangian density of relativistic mean field (RMF) theory is proposed, which provides an excellent description of nuclear properties, including those far from the valley of beta-stability and recently measured superdeformed minima in the Hg region. RMF theory, with a limited number of parameters, successfully describes nuclear structure properties, including anomalous kinks in isotope shifts, giant resonances, and superdeformed rotational bands. However, existing parameterizations like NL1 and NL-SH have limitations, such as over-binding along the beta-stability line and poor description of superdeformed minima in Hg isotopes. The new parameterization, NL3, addresses these issues by improving the description of nuclear properties, including charge radii, binding energies, and deformation characteristics. NL3 predicts a nuclear matter incompressibility between that of NL1 and NL-SH, with an asymmetry energy closer to NL-SH. It successfully reproduces experimental data for nuclear masses, charge radii, and deformation properties of rare-earth and actinide nuclei. NL3 also accurately describes isoscalar giant monopole resonances in Pb and Zr nuclei, which previous parameterizations failed to do. The new parameterization is validated through detailed calculations for Sn isotopes and other nuclei, showing improved results over NL1 and NL-SH. The study concludes that NL3 provides a more accurate description of nuclear properties and can be used in future investigations alongside other parameterizations.