Relativistic effects on the nuclear magnetic shielding $\mathbit{\ensuremath{\sigma}}(M)$ of the series of diatomics $M\text{F}$ ($M=\text{Cu}$, Ag, Au) are calculated and analyzed using the Dirac-Hartree-Fock (DHF) method in the random phase approximation (RPA). Significant differences due to relativistic effects on the shielding constant $\mathbit{\ensuremath{\sigma}}(M)$ are found in this series of atoms. The high electronegativity of the fluorine atom works in conjunction with the spin-orbit coupling to increase the calculated value for $\mathbit{\ensuremath{\sigma}}(\text{Au})$. An unusually large diamagnetic contribution to the shielding constant is observed. Nonrelativistic nuclear magnetic shielding $[{\mathbit{\ensuremath{\sigma}}}^{\text{NR}}(M)]$ shows very good linear correlation with the nuclear charge ($Z$) of the metal, while the relativistic shielding $[{\mathbit{\ensuremath{\sigma}}}^{\text{rel}}(M)]$ varies as ${Z}^{2.26}$.