The role of the relative motions of protons on different chain segments in the relaxation of the dipolar coupling measured in nuclear magnetic resonance experiments is considered. The relaxation of the coupling for a single intersegmental proton-proton pair is evaluated numerically, assuming that the decay of this coupling is dominated by the translational motion of the monomers. It is found that the relaxation of this coupling scales as g(r)(t)(-5/2), where g(r)(t) is the mean squared relative displacement of two monomers in the melt. This scaling applies for times at which g(r)(t) is greater than the square of the initial separation of the two coupled protons. The effect of the short range equilibrium structure of the melt on the intersegmental relaxation is qualitatively considered by separating out, from the summation over all interactions, the interactions between the protons corresponding to the first intersegmental peak in the hydrogen-hydrogen radial distribution function. This analysis indicates that the short range melt structure results in a more rapid decay of the intersegmental interactions at moderately short times, than would be predicted if the short range structure is ignored.