Although the dielectric beta glass-rubber relaxation has previously been observed in dipole-decorated branched polyethylenes and in linear polyethylene containing several mole per cent chlorine, it has not been observed in linear polyethylene containing very low dipole concentrations. Dielectric relaxation has been studied here in a linear polyethylene specimen (containing a few carbonyl groups per 1000 methylene units) in the hope of observing the beta process. The isochronal loss peak for the beta relaxation is not well resolved from that for the alpha relaxation. However, it is found that the beta process is very apparent as an increment in the isochronal dielectric constant scans. This was taken advantage of in characterizing the relaxation. In comparing the results with previous work it is found that there is a progression in the beta relaxation T(max) location towards higher temperature as the degree of crystallinity increases through branched and linear polyethylene specimens.