We describe a novel technique for measuring the basal melt rate at a point on an ice shelf. The method uses a phase-sensitive radar to observe the change in thickness of the ice column between an upper reference horizon and the ice shelf base. The observed thickness change is a combination of basal melting, horizontal ice divergence and firn compaction. The latter two components are determined independently by the repeat survey of surface markers and from estimates of surface accumulation rate and density at the depth of the reference horizon. The technique has been applied at a site on George VI Ice Shelf, Antarctica, where a melt rate of 2.78 ¿ 0.08 m yr-1 was observed over a twelve-day period. Our technique is applicable to almost any ice shelf or floating glacier tongue, and its high precision over short time intervals will permit the measurement of seasonal variations in melt rate.