A new PGSE NMR experiment, designed to measure molecular diffusion coefficients in systems with nonvanishing static dipolar coupling, is described. The fast static dipolar dephasing of the single-quantum ¹³C coherences is removed by multiple-pulse heteronuclear decoupling. The resulting slow dephasing of the ¹³ coherences allows for inserting appropriate gradient pulses into the pulse sequence. The presence of the large magnetic field gradient reduces the efficiency of the decoupling sequences which is compensated for by introducing a scheme of sequential slice selection across the sample. The method is demonstrated by ¹⁹F-decoupled ¹³C PGSE NMR experiments in a lyotropic nematic and lamellar liquid crystal.